Processus spatialement dépendants : convergence vers la normalité, tests d'association et applications
Thèses d'Orsay, no. 256 (1989) , 230 p.
@phdthesis{BJHTUP11_1989__0256__A1_0,
     author = {Richardson-Lamblin, Sylvia},
     title = {Processus spatialement d\'ependants : convergence vers la normalit\'e, tests d'association et applications},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e Paris-Sud Centre d'Orsay},
     number = {256},
     year = {1989},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_1989__0256__A1_0/}
}
TY  - BOOK
AU  - Richardson-Lamblin, Sylvia
TI  - Processus spatialement dépendants : convergence vers la normalité, tests d'association et applications
T3  - Thèses d'Orsay
PY  - 1989
IS  - 256
PB  - Université Paris-Sud Centre d'Orsay
UR  - http://www.numdam.org/item/BJHTUP11_1989__0256__A1_0/
LA  - fr
ID  - BJHTUP11_1989__0256__A1_0
ER  - 
%0 Book
%A Richardson-Lamblin, Sylvia
%T Processus spatialement dépendants : convergence vers la normalité, tests d'association et applications
%S Thèses d'Orsay
%D 1989
%N 256
%I Université Paris-Sud Centre d'Orsay
%U http://www.numdam.org/item/BJHTUP11_1989__0256__A1_0/
%G fr
%F BJHTUP11_1989__0256__A1_0
Richardson-Lamblin, Sylvia. Processus spatialement dépendants : convergence vers la normalité, tests d'association et applications. Thèses d'Orsay, no. 256 (1989), 230 p. http://numdam.org/item/BJHTUP11_1989__0256__A1_0/

(1) Chacon, R.V. A geometric construction of measure preserving transformations, Proc. Fifth Berkeley Sym. Math. Stat. Prob., University of California Press, 1967, Vol II, part 2, 335-360. | MR | Zbl

(2) Friedman, N.A. Introduction to Ergodic Theory. New York : van Nostrand 1970 | MR | Zbl

(3) Friedman, N.A. Bernoulli shifts induce Bernoulli shifts. Advances in Math. 10, 39-48 (1970) | MR | Zbl | DOI

(4) Friedman, N.A., Ornstein, D.S. Ergodic transformations induce mixing transformations. Advances in Math. 10, 147-163 (1973) | MR | Zbl | DOI

(5) Halmos, P.R. Lectures on Ergodic Theory. New-York - Chelsea 1956. | MR | Zbl

(6) Neveu J. Temps d'arrêt d'un système dynamique. Z. Wahrscheinlichkeitstheorie verw. Gebiete 13, 81-94 (1969). | MR | Zbl | DOI

(7) Ornstein, D.S., Smorodinski, M. Ergodic flows of positive entropy can be time changed to become K.flows. Israel J. Math. 26, 75-83 (1977). | MR | Zbl | DOI

(8) Shields, P. Cutting and independent stacking of intervals. Math. Systems Theory 7, 1-4 (1973). | MR | Zbl

(9) Walters, P. An Introduction to Ergodic Theory. Graduate Text in Mathematics. Vol 79 New-York, Springer Verlag 1981. | Zbl | MR

(1) Anderson, T.W. The statistical analysis of time series. New York : Wiley (1971). | MR | Zbl

(2) Bartlett, M.S. Some aspects of the time-correlation problem in regard to tests of significance. Journal of the Royal Statistical Society, 98, 536-543 (1935). | JFM | Zbl | DOI

(3) Bartlett, M.S. An Introduction to Stochastic Processes, 2nd edition Cambridge University Press 1966. | MR | Zbl

(4) Bolthausen, E. On the central limit theorem for stationary random fields. Ann. Probability 10, 1047-1050 (1982). | MR | Zbl

(5) Cliff, A.D. and Ord, J.K. Model building and the analysis of spatial pattern in human geography. Journal of the Royal Statistical Society B, 37, 297-348 (1975). | MR | Zbl

(6) Dobrushin, R.L. The description of a random field by its conditional distribution and its regularity condition. Theory Probability Appl. 13, 197-227 (1968). | Zbl

(7) Guyon, X. Estimation par pseudo-vraisemblance conditionnelle pour les champs : étude asymptotique et application aux champs markoviens. Proceedings of the 6th Franco-Belgian Meeting of Statisticians, November 1985. Edited by F. Droesbeke. Travaux et Recherches Vol 11, p. 15-62. Publications des Facultés universitaires St Louis, Bruxelles. | MR

(8) Hall, P., Heyde, C.C. Martingale limit theory and its application. New York : Academic Press 1980. | MR | Zbl

(9) Hannan, E.J. Multiple Times Series. New York : Wiley 1970. | MR | Zbl

(10) Haugh, L.D. and Box, G.E.P. Identification of dynamic regression (distributed lag) models connecting two time series. J. Amer. Statist. Assoc. 72, 121-130 (1977). | MR | Zbl | DOI

(11) Heinrich, L. Asymptotic expansions in the Central Limit Theorem for a special class of m-dependent random fields. Mathematische Nachrichten 83-106 (1987). | MR | Zbl

(12) Ibragimov, I.A., Linnik, Yu.V. Independent and stationary sequences of random variables. Groningen : Wolters-Nordhoff 1971. | MR | Zbl

(13) Johnston, J. Econometric Methods, 2nd edition. New York : McGrawHill 1972.

(14) Künsch, H.R. Reelwertige Zufallsfelder anf einem Gitter : Interpolation, variations sprinzip und Stat. Analyse, Thèse E.T.H. de Zurich, 1980.

(15) Künsch, H.R. Decay of correlations under Dobrushin's uniqueness condition and its applications. Comm. Math. Phys. 84, 207-222 (1982). | MR | Zbl | DOI

(16) Prakasa Rao, B.L. A non uniform estimates of the rate of convergence in the central limit theorem for m-dependent random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 58, 247-256 (1981). | MR | Zbl | DOI

(17) Rosenblatt, M. Stationary sequences and random fields. Boston : Birkhäuser 1985. | MR | Zbl | DOI

(18) Shergin, V.V. An estimate of the remainder term in the central limit theorem for m-dependent random variables. Theory Probability Appl. 24, 782-796 (1979). | Zbl

(19) Takahata, H. On the rates in the central limit theorem for weakly dependent random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 64, 445-456 (1983). | MR | Zbl | DOI

(20) Tempelman, A.A. Ergodic theorems for dynamical systems. Trans. Moscow Math. Soc. 26, 94-132 (1972). | Zbl

(21) Tikhomirov, A.N. On the converge rate in the centra limit theorem for weakly dependent random variables. Theory Probability Appl. 25, 790-809 (1980). | Zbl

(22) Tjøstheim, D. A measure of association for spatial variables. Biometrika 65, 109-114 (1978). | MR | Zbl | DOI

(23) Withers, C.S. Conditions for linear processes to be strong mixing. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 477-480 (1981). | MR | Zbl | DOI

(1) S.T. Richardson, K.M. Wilkinson Stopping time transformations and towers. Z. Wahrscheinlichkeitstheorie verw. Gebiete 48. 259-284, (1979) | MR | Zbl | DOI

(2) S.T. Richardson Stopping times for measure-preserving transformations : some approximation results. Proceedings of the London Mathematical Society (3) 43 : 273-294 (1981). | MR | Zbl | DOI

(3) S.T. Richardson, D. Hémon On the variance of the sample correlation between two independent lattice processes. J. Appl. Prob. 18, 943-948 (1981). | MR | Zbl | DOI

(4) S.T. Richardson, D. Hémon Autocorrélation spatiale : ses conséquences sur la corrélation empirique de deux processus spatiaux. Revue de Statistique Appliquée, 30 : 41-51 (1982).

(5) X. Guyon, S.T. Richardson Vitesse de convergence du théorème de la limite centrale pour des champs faiblement dépendants. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 66 : 297-314 (1984). | MR | Zbl | DOI

(6) S.T. Richardson Testing the association between two spatial processes : a review of different approaches Spatial processes and spatial time series analysis. Proceedings of the 6th Franco-Belgian Meeting of Statisticians, November 1985. Edited by F. Droesbeke. Travaux et Recherches Vol 11, p. 193-200. Publications des Facultés universitaires St Louis, Bruxelles. | MR

(7) P. Clifford, S.T. Richardson, D. Hémon Assessing the significance of the correlation between two spatial processes. Biometrics, 45 : 123-134 (1989). | MR | Zbl | DOI

(8) S.T. Richardson, P. Clifford Testing association between spatial processes. A paraître dans Proceedings of the A.M.S conference on Spatial Statistics and Imaging (June 1988).

(9) S.T. Richardson A method for testing the significance of geographical correlations with application to industrial lung cancer in France. A paraître dans Statistics in Medecine.

(10) S.T. Richardson, I. Stücker, D. Hémon Comparison of relative risks obtained in ecological and individual studies : some methodological considerations. International Journal of Epidemiology, Vol 16, n°1, 111-120 (1987). | DOI

1. Friedman. N.A. : Introduction to Ergodic Theory. New York: van Nostrand1970 | MR | Zbl

2. Friedman. N.A.: Bernoulli shifts induce Bernoulli shifts. Advances in Math. 10. 39-48 (1970) | MR | Zbl | DOI

3. Friedman. N.A.. Orstein. D.S.: On isomorphism of weak Bernoulli transformations. Advances in Math. 5. 365-394 (1970) | MR | Zbl | DOI

4. Neveu. J.: Temps d'arrêt d'un système dynamique. Z. Wahrscheinlichkeitstheorie verw. Gebiete 13. 81-94 (1969) | MR | Zbl | DOI

5. Ornstein. D.S.: Bernoulli shifts with infinite entropy are isomorphic. Advances in Math. 5. 339-348 (1970) | MR | Zbl | DOI

6. Saleski. A.: Stopping times for Bernoulli automorphisms. Pacific J. Math. 52. 547-551 (1974) | MR | Zbl | DOI

7. Shields. P.: Cutting and Independent Stacking of Intervals. Math. Systems Theory 7. 1-4 (1973) | MR | Zbl

1. R. M. Belinskaya. 'Partitions of Lebesgue space in trajectories defined by ergodic automorphisms'. Funkcional. Anal. i Prilozen 2 (1968) 4-16 | Zbl

R. M. Belinskaya. 'Partitions of Lebesgue space in trajectories defined by ergodic automorphisms'. Functional Anal. Appl.2 (1968) 190-99.

2. R. M. Belinskaya. 'Generalised degrees of automorphism and entropy', Sibirsk. Mat. Ž. 11 (1970) 739-49 | MR | Zbl

R. M. Belinskaya. 'Generalised degrees of automorphism and entropy', Siberian Math. J.11 (1970) 559-66. | Zbl | DOI

3. N. A. Friedman. Introduction to ergodic theory (van Nostrand. New York, 1970). | MR | Zbl

4. N. A. Friedman and D. S. Ornstein. 'Ergodic transformations induce mixing transformations'. Adv. in Math. 10 (1973) 147-63. | MR | Zbl | DOI

5. S. Kakutani. 'Induced measure preserving transformations'. Proc. Imp. Acad. Sci. Tokyo 19 (1943) 635-41. | MR | Zbl

6. J. Neveu. 'Temps d'arrêt d'un système dynamique', Z. Wahrsch. Verw. Gebiete 13 (1969) 81-94. | MR | Zbl | DOI

7. D. S. Ornstein and M. Smorodinsky. 'Ergodic flows of positive entropy can be time changed to become K-flows', Israel J. Math. 26 (1977) 75-83. | MR | Zbl | DOI

8. S. T. Richardson and K. M. Wilkinson, 'Stopping time transformations and towers', Z. Wahrsch. Verw. Gebiete 48 (1979) 259-84. | MR | Zbl | DOI

9. V. A. Rohlin, 'Lectures on the entropy theory of measure preserving transformations', Uspehi Mat. Nauk 22 (1967) 3-56

9. V. A. Rohlin, 'Lectures on the entropy theory of measure preserving transformations', Russian Math. Surveys 22 (1967) 1-52. | Zbl | DOI

Abramowitz. M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover. New York. | MR

Bartlett, M. S. (1935) Some aspects of the time-correlation problem in regard to tests of significance. J. R. Statist. Soc. 98, 536-543. | JFM | Zbl | DOI

Bartlett, M. S. (1966) An Introduction to Stochastic Processes, 2nd edn. Cambridge University Press. | MR | Zbl

Bennett, R. J. (1980) Spatial Time Series. Pion, London. | MR

Besag, J. E. (1972) On the correlation structure of some two-dimensional stationary processes. Biometrika 59. 43-48. | MR | Zbl | DOI

Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B 36. 192-236. | MR | Zbl

Hannan. E. J. (1970) Multiple Time Series. Wiley, New York. | MR | Zbl

Haugh, L. D. and Box, G. E. P. (1977) Identification of dynamic regression (distributed lag) models connecting two time series. J. Amer. Statist. Assoc. 72. 121-130. | MR | Zbl | DOI

Moran, P. A. P. (1973a) A Gaussian Markovian process on a square lattice. J. Appl. Prob. 10. 54-62. | MR | Zbl | DOI

Moran. P. A. P. (1973b) Necessary conditions for Markovian processes on a lattice. J. Appl. Prob. 10. 605-612. | MR | Zbl | DOI

Pierce, D. A. (1979) 𝐑 2 measures for time series J. Amer. Statist. Assoc. 74. 901-910. | MR | Zbl

Quenouille, M. H. (1947) Notes on the calculation of autocorrelations of linear autoregressive schemes. Biometrika 34. 365-367. | MR | Zbl | DOI

Rozanov. Yu. A. (1967) On the Gaussian homogeneous fields with given conditional distributions. Theory Prob. Appl. 12. 381-391. | Zbl

Tjøstheim. D. (1978) Statistical spatial series modelling. Adv. Appl. Prob. 10. 130-154. | MR | Zbl

Whittle, P. (1954) On stationary processes in the plane. Biometrika 41. 434-449. | MR | Zbl | DOI

[1] M. Abramowitz and I.A. Stegun. - Handbook of Mathematical Functions. Dover, New-York, 1965. | MR

[2] M.S. Bartlett. - Some aspects of the time-correlation problem in regard to tests of significance. J.R. Statist. Soc.,98, 536-543, 1935. | JFM | Zbl | DOI

[3] M.S. Bartlett. - An Introduction to Stochastic Processes, 2nd edn. Cambridge University Press, Cambridge, 1966. | MR | Zbl

[4] R.J. Bennett. - Spatial Time Series. Pion, London, 1980. | MR | Zbl

[5] J.E. Besag. - On the correlation structure of some two-dimensional stationary processes. Biometrika, 59, 43-48, 1972. | MR | Zbl | DOI

[6] J.E. Besag. - Spatial interaction and the statistical analysis of lattice system (with discussion) J.R. Statist, Soc., B 36, 192-236, 1974. | MR | Zbl

[7] J.E. Besag and P.J. Diggle. - Simple Monte Carlo tests for spatial pattern. J.R. Statist. Soc., C 26, 327-333, 1977.

[8] A.D. Cliff and J.K. Ord. - Model building and the analysis of spatial pattern in human geography (with discussion). J.R. Statist. Soc., B 37, 297-348, 1975. | MR | Zbl

[9] A.D. Cliff and J.K. Ord. - The effects of spatial autocorrelation on geographical modelling. University of Warwick Technical Report, 1978.

[10] L. Curry. - A bivariate spatial regression operator. Canadian Geographer, 16, 1-14, 1972. | DOI

[11] C.W.J. Granger. - Spatial data and time series analysis. In Studies in Regional Sciences (A.J. Scott, ed), 1-24. London : Pion, 1969.

[12] X. Guyon et B. Prum. - Estimations et tests relatifs aux processus spatiaux réguliers du second ordre, Publication n° 201, Université d'Orsay, 1976.

[13] E.J. Hannan. - Multiple Time Series. John Wiley and Sons, New-York, 1970. | MR | Zbl

[14] L.D. Haugh and G.E.P. Box. - Identification of dynamic regression (distributed lag) models connecting two time series. J. Amer. Statist. Assoc., 72, 121-130, 1977. | MR | Zbl | DOI

[15] L. Lebart. - Analyse statistique de la continguité. Pub. Inst. Stat. Univ. Paris, 18, 81-112, 1969. | Zbl

[16] R.J. Martin. - A subclass of lattice processes applied to a problem in planar sampling. Biometrika, 66, 209-17, 1979. | MR | Zbl | DOI

[17] R.L. Martin. - On spatial dependence, bias, and the use of first spatial differences in regression analysis. Area, 6, 185-94, 1974.

[18] P.A.P. Moran. - A Gaussian Markovian process on a square lattice. J. Appl. Prob., 10, 54-62, 1973. | MR | Zbl | DOI

[19] P.A.P. Moran. - Necessary conditions for Markovian processes on a lattice. J. Appl. Prob., 10, 605-612, 1973. | MR | Zbl | DOI

[20] J.K. Ord. - Estimation methods for models of spatial interaction. J. Am. Statist. Assoc., 70, 120-6, 1975. | MR | Zbl | DOI

[21] D.A. Pierce. - 𝐑 2 Measures for time series. J. Amer. Statist. Assoc., 74, 901-910, 1979. | MR | Zbl

[22] D.A. Pierce and L.D. Haugh. - Causality in temoral systems, characterizations and a survey. J. Econometrics, 5, 265-293, 1977. | MR | Zbl | DOI

[23] S.T. Richarson and D. Hemon. - On the variance of the sample correlation between two independant lattice processes. J. Appl. Prob., 18, 943-8, 1981. | MR | Zbl | DOI

[24] Yu. A. Rozanov. - On the Gaussian homogeneous fields with given conditional distributions. Theor. Prob. Appl., 12, 381-391, 1967. | Zbl

[25] D. Tjostheim. - Statistical spatial series modelling. Adv. Appl. Probl., 10, 130-154, 1978. | MR | Zbl

[26] D.J. Unwin and L.W. Hepple. - The statistical analysis of spatial series. The Statistician, 23, 211-27, 1974. | DOI

[27] P. Whittle. - On stationary processes in the plane. Biometrika, 41, 434-449, 1954. | MR | Zbl | DOI

1. Berkes. I., Morrow, G.J.: Strong invariance principales for mixing random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 13-37 (1981) | MR | Zbl | DOI

2. Bolthausen. E.: Exact convergence rates in some martingale central limit theorem. Ann. Probability 10. 672-688 (1982) | MR | Zbl

3. Bolthausen. E.: On the central limit theorem for stationary random fields. Ann. Probability 10, 1047-1050 (1982) | MR | Zbl

4. Bolthausen. E.: The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Z. Wahrscheinlichkeitstheorie verw. Gebiete 60. 283-289 (1982) | MR | Zbl | DOI

5. Deo. C.M.: A functional central limit theorem for stationary random fields. Ann. Probability 3, 708-715 (1975) | MR | Zbl

6. Doukhan. P., Portal. F.: Principes d'invariance faibles, avec vitesse dans un cadre mélangeant. Prépublication Orsay n° 83T28 (1983)

7. Dobrushin, R.L.: The description of a random field by its conditional distribution and its regularity condition. Theory Probability Appl. 13, 197-227 (1968) | Zbl

8. Egorov, V.A.: Certain limit theorems for m-dependent random variables. Liet. Mat. Rink 10, 51-59 (1970) (en Russe) | MR | Zbl

9. Gorodetskii, V.V.: The invariance principle for stationary random fields satisfying the strong mixing condition. Theory Probability Appl. 27. 380-385 (1982) | Zbl | MR

10. Ibragimov, I.A., Linnik, Yu.V.: Independent and stationary sequences of random variables. Groningen: Wolters-Nordhoff 1971 | MR | Zbl

11. Hall, P., Heyde. C.C.: Martingale limit theory and its application. New York: Academic Press 1980 | MR | Zbl

12. Leonenko, N.N.: Estimate of the rate of convergence in the central limit theorem for m-dependent random fields. Mathematical Notes 17, 76-78 (1975) | Zbl | MR

13. Maejima: A non uniform estimate in the central limit theorem for m-dependent random variables. Keio Engineering Reports 31. 15-20 (1978) | MR | Zbl

14. Nahapetian, B.S.: The central limit theorem for random fields. In Multicomponent Random Systems, pp. 531-542. ed. by R.L. Dobrushin and Ya.G. Sinai. New York: Marcel Dekker 1980 | MR

15. Neaderhauser, C.C.: Limit theorems for multiply indexed mixing random variables, with application to Gibbs random fields. Ann. Probability 6. 207-215 (1978) | MR | Zbl

16. Neaderhauser, C.C.: Some limit theorems for random fields. Comm. Math. Phys. 61. 293-305 (1978) | MR | Zbl | DOI

17. Petrov, V.V.: On the central limit theorem for m-dependent variables. Selected Transl. Math. Statist. Probability 9. 83-88 (1970) | Zbl

18. Prakasa Rao, B.L.: A non uniform estimate of the rate of convergence in the central limit theorem for m-dependent random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 58. 247-256 (1981) | MR | Zbl | DOI

19. Schneider, E.: On the speed of convergence in the random central limit theorem of ø-mixing processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 58, 125-138 (1981) | MR | Zbl | DOI

20. Shergin, V.V.: An estimate of the remainder term in the central limit theorem for m-dependent random variables. Lith. Math. J. vol 16, 637-641 (1977) (trad. de Litov Math. Sbornik, vol. 15, 245-250 (1976) | Zbl | MR

21. Shergin, V.V.: On the convergence rate in the central limit theorem for m-dependent random variables. Theory Probability Appl. 24. 782-796 (1979) | Zbl

22. Stein, C.: A Bound for the error in the normal approximation of a sum of dependent random variables. Proc. Berkeley Sympos. Math. Statist Probability 2, 583-603 Univ. Calif. (1972) | MR | Zbl

23. Takahata, H.: On the rates in the central limit theorem for weakly dependent random fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 64. 445-456 (1983) | MR | Zbl | DOI

24. Tikhominov, A.N.: On the converge rate in the central limit theorem for weakly dependent random variables. Theory Probability Appl. 25. 790-809 (1980) | Zbl

25. Yokoyama, R.: Moment bounds for stationary mixing sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 52. 45-57 (1980) | MR | Zbl | DOI

[1] Agterberg, F.P. (1984), "Trend surface analysis", in Spatial Statistics and Models, edited by E.L. Gaile and C.J. Willmott. Dordrecht, Reidel. | DOI

[2] Arora, S.S. and M. Brown (1977), "Alternative approaches to spatial autocorrelation : an improvement over current practice". International Regional Science Review, 2(1). | DOI

[3] Bartlett, M.S. (1935), "Some aspects of time-correlation problem in regard to test of significance". Journal of the Royal Statistical Society, 98, 536-543. | JFM | Zbl | DOI

[4] Bennett, R.J. (1979), Spatial Time Series. London, Pion. | MR | Zbl

[5] Besag, J.E. (1975), "Statistical analysis of non-lattice data". The Statistician, 24(3), 179-195. | DOI

[6] Besag, J.E. and P.J. Diggle (1977), "Simple Monte Carlo tests for spatial pattern". Applied Statistics, 26(3), 327-333.

[7] Bivand, R.S. (1980), "A Monte Carlo study of correlation coefficient estimation with spatially autocorrelated observations". Quaestiones Geographicae, 6, 5-10.

[8] Bivand, R.S. (1984), "Regression modeling with spatial dependence : an application of some class selection and estimation methods". Geographical Analysis, 16(1), 25-37.

[9] Bodson, P. and D. Peeters (1975), "Estimation of the coefficients of a linear regression in the presence of spatial autocorrelation. An application to a Belgian labour-demand function". Environment and Planning A, 7, 456-472. | DOI

[10] Brandsma, A.S. and R.H. Ketellapper (1979), "Further evidence on alternative procedures for testing of spatial autocorrelation among regression disturbances", in Exploratory and Explanatory Statistical Analysis of Spatial Data, edited by Bartels and Ketellapper. | DOI

[11] Burridge, P. (1981), "Testing for a common factor in a spatial autogresssion model". Environment and Planning A, 13, 795-800. | DOI

[12] Cliff, A.D. and J.K. Ord (1981), Spatial Processes. Models and Applications. London, Pion. | MR | Zbl

[13] Clifford, P. and S. Richardson (1985), "Testing the association between two spatial processes". Statistics and Decisions, Suppl. issue, 2, 155-160. | MR

[14] Cook, D.G. and S.J. Pocock (1983), "Multiple regression in geographic mortality studies with allowance for spartially correlated errors". Biometrics, 39, 361-371. | DOI

[15] Cox, D.R. (1981), "Statistical analysis of time series : some recent developments". Scandinavian Journal of Statistics, 8, 93-115. | MR | Zbl

[16] Doll, R. (1980), "The epidemiology of cancer". Cancer, 45, 2475-2485.

[17] Doreian, P. (1981), "Estimating linear models with spatially distributed data", in Sociological Methodology, edited by Leinhardt and Samuel. San Francisco, Jossey-Bass Publishers, 359-388. | DOI

[18] Geweke, J. (1981), "A comparison of tests of the independence of two covariance- stationary time series". Journal of the American Statistical Association, 76(374), 363-373. | MR | Zbl | DOI

[19] Glick, B.J. (1982), "A spatial rank order correlation measure". Geographical Analysis, 14(2), 177-181. | DOI

[20] Griffith, D.A. (1980), "Towards a theory of spatial statistics". Geographical Analysis, 12(4), 325-339. | DOI

[21] Haining, R. (1985), "Income diffusion and regional economic structure". Presented to the NATO advanced studies institute, Hanstholm, Denmark.

[22] Haining, R. (1985), "Trend surface models with global and local scales of variation". Presented at a conference on Applied Spatial Statistics, Cambridge College of Arts and Technology, April 18, 1985.

[23] Haugh, L.D. (1976), "Checking the independence of two covariance-stationary time series : a univariate residual crosscorrelation approach". Journal of the American Statistical Association, 71, 378-385. | MR | Zbl | DOI

[24] Hepple, L.W. (1984), "Bayesian analysis of the linear model with spatial dependence", in Spatial Statistics and Models, edited by Gaile and Reidel. Dordrecht, Reidel.

[25] Hubert, L.J. and R.G. Golledge (1982), "Measuring association between spatially defined variables : Tjøstheim's index and some extensions". Geographical Analysis, 14(3), 273-278. | DOI

[26] Johnston, J. (1972), Econometric Methods, 2nd edition. New York, McGraw Hill.

[27] Lebart, L. (1969), "Analyse statistique de la contiguité". Publ. Int. Stat. Univ. Paris, 18, 81-112. | Zbl

[28] Mardia, K.V. and R.J. Marsnall (1984), "Maximum likelihood estimation of models for residual covariance in spatial regression". Biometrika, 71(1), 135-146. | MR | Zbl | DOI

[29] Martin, R.L. (1974), "On spatial dependence, bias, and the use of first spatial differences in regression analysis". Area, 6, 185-194.

[30] Ord, K. (1975), "Estimation methods for models of spatial interaction". Journal of the American Statistical Association, 70, 120-125. | MR | Zbl | DOI

[31] Pierce, D.A. (1977), "Relationships and the lack thereof between economic time series, with special reference to money and interest rates". Journal of the American Statistical Association, 72(357), 11-26.

[32] Richardson, S. and D. Hémon (1981), "On the variance of the same correlation between two independent lattice processes". Journal of Applied Probability, 18, 943-948. | MR | Zbl | DOI

[33] Richardson, S. and D. Hémon (1982), "Autocorrélation spatiale : ses conséquences sur la corrélation empirique de deux processus spatiaux". Revue de Statistique Appliquée, 30(1), 41-51.

[34] Ripley, B.D. (1981), Spatial Statistics. New York, Wiley. | MR | Zbl

[35] Streitberg, B. (1979), "Multivariate models of dependent spatial data", in Exploratory and Explanatory Statistical Analysis of Spatial Data, edited by Bartels and Ketellapper. | DOI

[36] Tjøstheim, D. (1978), "A measure of association for spatial variables". Biometrika, 66(1), 109-114. | MR | Zbl | DOI

[37] Upton, G. and B. Fingleton (1983), Spatial Data Analysis by Example. New York, Wiley. | MR

Armstrong, B. and Doll, R. (1975). Environmental factors and cancer incidence and mortality in different countries, with special reference to dietary practices. International Journal of Cancer 15, 617-631. | DOI

Bartlett. M. S. (1935). Some aspects of the time-correlation problem in regard to tests of significance. Journal of the Royal Statistical Society 98, 536-543. | JFM | Zbl | DOI

Bartlett, M. S. (1978). Nearest neighbour models in the analysis of field experiments. Journal of the Royal Statistical Society, Series B 40, 147-174 | MR | Zbl

Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 36, 192-236. | MR | Zbl

Cliff. A. D. and Ord, J. K. (1975). Model building and the analysis of spatial pattern in human geography. Journal of the Royal Statistical Society, Series B 37, 297-348. | MR | Zbl

Clifford. P. and Richardson, S. (1985). Testing the association between two spatial processes. Statistics and Decisions. Supp. issue 2, 155-160. | MR

Cook. D. G. and Pocock, S. J. (1983). Multiple regression in geographic mortality studies with allowance for spatially correlated errors. Biometrics 39, 361-371. | DOI

Davies. H. M. and Jowett. G. H. (1958). The fitting of Markoff serial variation curves. Journal of the Royal Statistical Society. Series B 20, 120-142. | MR | Zbl

Granger. C. W. J. (1969). Spatial data and time series analysis. In London Papers in Regional Science 1. Studies in Regional Science. A. J. Scott (ed.). 1-24. London: Pion

Haugh. L. D. (1976). Checking the independence of two covariance stationary time series: A univariate residual cross-correlation approach. Journal of the American Statistical Association 71, 378-385. | MR | Zbl | DOI

Hoover. R. and Fraumeni. J. F. (1975). Cancer mortality in U.S. counties with chemical industries. Environmental Research 9, 196-207. | DOI

Hubert. L. J. and Golledge. R. G. (1982). Measuring association between spatially defined variables: Tjostheim's index and some extensions. Geographical Analysis 14, 273-278. | DOI

Mardia. K. V. and Marshall. R. J. (1984). Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71, 135-146. | MR | Zbl | DOI

Ord, K. (1975). Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70, 120-126. | MR | Zbl | DOI

Richardson. S. and Hémon, D. (1981). On the variance of the sample correlation between two independent lattice processes. Journal of Applied Probability 18, 943-948. | MR | Zbl | DOI

Ripley, B. D. (1981). Spatial Statistics. New York: Wiley. | MR | Zbl

Schottenfeld. D. and Fraumeni, J. F. (1982). Cancer Epidemiology and Prevention. Philadelphia: W. B. Saunders.

Student (W. S. Gosset) (1914). The elimination of spurious correlation due to position in time or space. Biometrika 10, 179-181. | DOI

Tjøstheim, D. (1978). A measure of association for spatial variables. Biometrika 65. 109-114. | MR | Zbl | DOI

Whittle, P. (1954). On stationary processes in the plane. Biometrika 41, 434-449. | MR | Zbl | DOI

- Cliff, A.D. and J.K. Ord (1981), Spatial Processes. Models and Applications. London, Pion. | MR | Zbl

- Clifford, P. Richardson, S. and Hémon, D. Assessing the significance of the correlation between two spatial processes, (1989) to appear in Biometrics. | MR | Zbl | DOI

- Doll, R. (1980). The epidemiology of cancer. Cancer, 45, 2475-2485.

- Doreian, P. (1981), Estimating linear models with spatially distributed data, in Sociological Methodology, edited by Leinhardt and Samuel. San Francisco, Jossey-Bass Publishers, 359-388. | DOI

- Malin, S.R.C. and Hide, R. (1982). Bumps on the core-mantle boundary : geomagnetic and gravitational evidence revisted. Phil. Trans. R. Soc. Lon A, 306, 281-289. | DOI

- Ripley, B.D. (1981), Spatial Statistics. New York, Wiley. | MR | Zbl

(1) Doll, R. The epidemiology of cancer. Cancer, 45,2475-85 (1980).

(2) Doll, R. ed. The geography of disease. British Medical Bulletin. Published for the British Council by Churchill Livingstone (1984).

(3) Hutt, M.S. and Burkitt, D.P. The geography of non-infectious disease. Oxford University Press Oxford (1986)

(4) Armstrong, B., Doll, R. Environmental factors and cancer incidence and mortality in different countries, with special reference to dietary practices. Int J Cancer, 15, 617-631 (1975). | DOI

(5) Blot, W.J. and Fraumeni, J.F. Geographic patterns of oral cancer in the United States : etiological implications. J Chron Dis, 30, 745-757 (1977) | DOI

(6) Graham, S. Methodological problems in ecologic studies of the asbestos cancer relationship. Envir Res, 25, 35-49 (1981) | DOI

(7) Cantor, K.P., Hoover, R., Mason, T.J, Mc Cabe, L.J. Associations of cancer mortality with halomethanes in drinking water. J Natl Cancer Inst, 61, 979-985 (1978).

(8) Cliff, A.D. and Ord, J.K. Spatial Processes. Models and Applications. London, Pion (1981). | MR | Zbl

(9) Doreian, P. "Estimating linear models with spatially distributed data", in Sociological Methodology, edited by Leinhardt and Samuel. San Francisco, Jossey-Bass Publishers, 359-388 (1981). | DOI

(10) Breslow, N.E. and Enstrom, J.E. Geographic correlations between cancer mortality rates and alcohol-tobacco consumption in the United States. J Natl Canc Inst, 53, 631-639 (1974). | DOI

(11) Stravraky, K.M. The role of ecologic anaysis in studies of the etiology of disease : a discussion with reference to large bowel cancer. J Chron Dis, 29, 435-444 (1976). | DOI

(12) Davies, J.M. and Chilvers, C. The study of mortality variations in small administrative areas of England and Wales, with special reference to cancer. J Epidem C, 34, 87-92 (1980). | DOI

(13) Morgenstern, H. Uses of ecological analysis in epidemiologic research. Am J Publ Health, 72, 1336-44 (1982). | DOI

(14) Richardson, S., Stücker, I., Hémon, D. Comparison of relative risks obtained in ecological and individual studies : some methodological considerations. Int J Epidemiol, 16, 111-120 (1987). | DOI

(15) Greenland, S., Morgenstern, H. Ecological bias, confounding, and effect modification. Int J Epidemiol, 18, 269-274 (1989). | DOI

(16) Pocock, S.J., Cook, D.G. and Shaaper, A.G. Analysing geographic variation in cardiovascular mortality : methods and results. J.R.Statist. Soc A, 145, 313-341 (1982). | DOI

(17) Clifford, P., Richardson, S. and Hémon, D. "Assessing the significance of the correlation between two spatial processes" Biometrics, 45(1), 123-134 (1989). | MR | Zbl | DOI

(18) Bartlett, M.S. Some aspects of the time-correlation problem in regard to tests of significance. J. R. Statist. Soc., 98, 536-543 (1935). | Zbl | JFM | DOI

(19) Johnston, J. Econometric Methods, 2nd edition. New York, McGrawHill (1972).

(20) Ord, K. Estimation methods for models of spatial interaction. J. Am. Statist. Ass, 70, 120-126 (1975). | MR | Zbl | DOI

(21) Mardia, K.V. and Marshall, R.J. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71, 135-146 (1984) | MR | Zbl | DOI

(22) Hepple, L.W. Bayesian analysis of the linear model with spatial dependence, in Exploratory and Explanatory Statistical Ananlysis of Spatial Data pp 179-199 (Bartels, C.P.A and Ketellapper, R.H., Eds). Martinus Mijhoff : Boston (1979). | DOI

(23) Warnes, J.J. and Ripley, B.D. Problems with likelihood estimation of covariance functions of spatial Gaussian processes. Biometrika, 74(3), 640-642 (1987). | MR | Zbl | DOI

(24) Ripley, B.D. Statistical inference for spatial processes. Cambridge University Press, Cambridge (1988). | MR | Zbl

(25) Cook, D.G. and Pocock, S.J. Multiple regression in geographic mortality studies with allowance for spatially correlated errors. Biometrics, 39, 361-371 (1983). | DOI

(26) Ripley, B.D. Spatial statistics. New York, Wiley (1981). | MR | Zbl

(27) Pastorino, U., Berrino, F., Gervasio, A., Pesenti, V., Riboli, E., Crosignomi, P. Proportion of lung cancers due to occupational exposure. Int J Cancer, 33, 231-237 (1984). | DOI

(28) Benhamou, S., Benhamou, E., Flamant, R. Occupational risk factors of lung cancer in a French case-control study. Br J Ind Med 45, 231-233, (1988).

(29) Simonato, L., Vineis, P. and Fletcher, A. Estimates of the proportion of lung cancer attributable to occupational exposure. Carcinogenesis, 9, 1159-1165 (1988). | DOI

1 Doll R. The epidemiology of cancer. Cancer 1980; 45: 2475-85.

2 Armstrong B. Doll R. Environmental factors and cancer incidence and mortality in different countries, with special reference to dietary practices. Int J Cancer 1975; 15: 617-31. | DOI

3 Blot Wj, Mason Tj, Hoover R, Fraumeni Jf. Cancer by county: etiologic implications. Origins of human cancer 1977.

4 Graham S. Methodological problems in ecologic studies of the asbestos cancer relationship. Envir Res 1981; 25: 35-49. | DOI

5 Cantor Kp, Hoover R, Mason Tj, Mccabe Lj. Associations of cancer mortality with halomethanes in drinking water. J Natl Canc Inst 1978; 61: 979-85.

6 Macmahon B, Pugh Tf. Epidemiology: principles and methods. Boston. Little Brown. 1970.

7 Breslow Ne. Enstrom Je. Geographic correlations between cancer mortality rates and alcohol-tobacco consumption in the United States. J Natl Canc Inst 1974: 53: 631-9. | DOI

8 Stravraky Km. The role of ecologic analysis in studies of the etiology of diseases: a discussion with reference to large bowel cancer. J Chron Dis 1976; 29: 435-44. | DOI

9 Davies Jm, Chilvers C. The study of mortality variations in small administrative areas of England and Wales, with special reference to cancer. J Epidemiol Community Health 1980; 34: 87-92. | DOI

10 Richardson St, Hémon D. On the variance of the sample correlation between two independent lattice processes. J Appl Prob 1981; 18: 943-8. | MR | Zbl | DOI

11 Cook Dg, Pocock Sj. Multiple regression in geographic mortality studies with allowance for spatially correlated errors. Biometrics 1983: 39: 361-71. | DOI

12 Cliff Ad, Ord Jk. Spatial processes, models and applications. London, Pion, 1981. | MR | Zbl

13 Morgenstern H. Uses of ecologic analysis in epidemiologic research. Am J Publ Health 1982; 72: 1336-44. | DOI

14 Béral V, Chilvers C, Fraser P. On the estimation of relative risk from vital statistical data. J Epidemiol Community Health 1979; 33: 159-62. | DOI

15 Kendall M. Stuart A. The advanced theory of statistics, vol 1, London. Charles Griffin, 1977. | Zbl

16 Robinson Ws. Ecological correlations and the behaviour of individuals. Am Sociol Rev 1950; 15: 351-57. | DOI

17 Goodman La. Some alternatives to ecological correlation. Am J Sociol 1959; 64: 610-25. | DOI

18 Thomas En. Anderson Dl. Additional comments on weighting values in correlation analysis of areal data. Annals of the Association of American Geographers 1965: 55: 492-505. | DOI

19 Alker Hr. A typology of ecological fallacies. In: M. Dogan and S. Rokkan (Eds) Quantitative ecological analysis in the social sciences, Cambridge, Ma, MIT Press, 1969.

20 Clark Wav. Avery Kl. The effects of data aggregation in statistical analysis. Geographical Analysis 1976; 8: 428-33.

21 Firebaugh G. A rule for inferring individual level relationship from aggregate data. Am Sociol Rev 1978; 43: 557-72. | DOI

22 Openshaw S. Ecological fallacies and the analysis of areal census data. Envir Pl-A 1984; 16: 17-31. | DOI

23 Finney Dj. Statistical methods in biological assay, London, Charles Griffin. 1952.

24 Doll R, Peto R. Avoidable risks of cancer in the U.S. J Natl Canc Inst 1981; 66: 1191-1308. | DOI

25 Damiani P, Massé H. Mortalité par cause et tabac: application d'un modèle de liaison et évaluation de la consommation de tabac par sexe et par âge. Journal de la Société de Statistique de Paris 1980; 121: 81-89.

26 Damiani P, Massé H. Liaison de la mortalité par cause avec l'ensemble des consommations de tabac et d'alcool. Journal de la Société de Statistique de Paris 1981; 122: 174-81.

27 Atlas of tobacco consumption in France, SEITA 1953-1957.

28 Etude du marché français du tabac. Enquête générale 1960. SEMA

29 U.S. Department Of Health And Human Services. The health consequences of smoking. Cancer: A report of the Surgeon General. Department of Health and Human Services, Public Health Service, Office on Smoking and Health, 1982.

30 Stocks P. Cancer mortality in relation to national consumption of cigarettes, solid fuel, tea and coffee. Br J Canc 1970; 24: 215-25. | DOI

31 World Health Statistics. Geneva, World Health Organization. 1979.

32 Lee Pn. Tobacco consumption in various countries. London, Tobacco Research Council, 1975.

33 Fraumeni J. Cigarette smoking and cancers of the urinary tract : geographic variation in the United States. J Natl Canc Inst 1968 ; 41 : 1205-11.

34 Lazar P. Geographical correlations between disease and environmental exposures. Proceedings of the European Symposium on Medical Statistics, Rome, 1980.

35 Wynder El. Goldsmith R. The epidemiology of bladder cancer. Cancer 1977 ; 40 : 1246-68.

36 Cartwright Ra. Adib R, Appleyard I et al. Cigarette smoking and bladder cancer : an epidemiological inquiry in West Yorkshire. J Epidemiol Community Health 1983; 37 : 256-63. | DOI

37 Howe Gr, Burch Jd, Miller Ab et al. Tobacco use, occupation, coffee, various nutrients, and bladder cancer. J Natl Canc Inst 1980 ; 64 : 701-13.

38 Vineis P, Frea B, Uberti E, Ghisetti V, Terracini B. Bladder cancer and cigarette smoking in males: a case-control study. Tumori 1983 ; 69 : 17-22. | DOI

39 Vineis P, Segnan N, Costa G, Terracini B. Evidence of a multiplicative effect between cigarette smoking and occupational exposures in the aetiology of bladder cancer. Cancer Let 1981 ; 14 : 285-90. | DOI

40 Kannel Wb, Framingham Md. Update on the role of cigarette smoking in coronary artery disease. Am Heart J 1981 ; 101 : 319-28. | DOI

41 Friedman Gd. Cigarette smoking and geographic variation in coronary heart disease mortality in the United States. J Chron Dis 1967 ; 20 : 769-79. | DOI

42 Dawber Tr. The Framingham study. Cambridge, Mass, Harvard University Press, 1980. | DOI

43 Wynder El, Bross Ij. A study of etiological factors in cancers of the oesophagus. Cancer 1961 ; 14 : 389-413.

44 Schwartz D, Flamant R, Lellouch J et al. Alcool et cancer. Résultats d'une étude rétrospective. Rev Fr Etudes Clin Biol 1962 ; 7 : 590-604.

45 Tuyns Aj. Péquignot G, Jensen Om. Le cancer de l'osophage en Ille et Vilaine en fonction des niveaux de consommation d'alcool et de tabac. Bulletin du cancer 1977 ; 64 : 1 : 45-60.

46 Tuyns A. Oesopheal cancer in non-smoking drinkers and in non-drinking smokers. Int J Canc 1983 ; 32 : 443-4. | DOI

47 Day Ne. The geographic pathology of cancer of the oesophagus. British Medical Bulletin 1984 ; 40 : 329-34. | DOI

48 Breslow Ne, Day Ne. The analysis of case-control studies. Lyon : IARC Scientific Publications no 32. 1980.