Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms
Annales de l'I.H.P. Probabilités et statistiques, Volume 29 (1993) no. 2, p. 289-319
@article{AIHPB_1993__29_2_289_0,
     author = {Johnstone, Iain M. and Macgibbon, K. Brenda},
     title = {Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {2},
     year = {1993},
     pages = {289-319},
     zbl = {0779.62022},
     mrnumber = {1227421},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1993__29_2_289_0}
}
Johnstone, Iain M.; Macgibbon, K. Brenda. Asymptotically minimax estimation of a constrained Poisson vector via polydisc transforms. Annales de l'I.H.P. Probabilités et statistiques, Volume 29 (1993) no. 2, pp. 289-319. http://www.numdam.org/item/AIHPB_1993__29_2_289_0/

J.O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd. ed., Springer Verlag, New York, 1985. | MR 804611 | Zbl 0572.62008

P.E. Berkin and B.Ya. Levit, Second-Order Asymptotically Minimax Estimates for the Mean of a Normal Population, Problemy Peredachi Informatsii, Vol. 16, 3, 1980, pp. 60-79. Translation: Problems of Information Transmission, 1981, pp. 212-229. | MR 624030 | Zbl 0466.62033

P.J. Bickel, Minimax Estimation of the Mean of a Normal Distribution when the Parameter Space is Restricted, Ann. Statist., Vol. 9, 1981, pp. 1301-1309. | MR 630112 | Zbl 0484.62013

L.D. Brown, Admissible Estimators, Recurrent Diffusions and Insoluble Boundary Value Problems, Ann. Math. Statist., Vol. 42, 1971, pp. 855-903. Correction, Ann. Statist., Vol. 1, pp. 594-596. | MR 286209 | Zbl 0246.62016

L.D. Brown, An Heuristic Method for Determining Admissibility of Estimators - with Applications, Ann. Statist., Vol. 7, 1979, pp. 960-994. | MR 536501 | Zbl 0414.62011

M. Clevenson and J. Zidek, Simultaneous Estimation of the Mean of Independent Poisson Laws, J. Amer. Statist. Assoc., Vol. 70, 1975, pp. 698-705. | MR 394962 | Zbl 0308.62018

R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, 1953. | MR 65391 | Zbl 0051.28802

E.N. Dancer, The Effect of Domain Shape on the Number of Positive Solutions of Certain Nonlinear Equations, J. Diff. Eq., Vol. 74, 1988, pp. 120-156. | MR 949628 | Zbl 0662.34025

D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin-Heidelberg, New York, 1983. | MR 737190 | Zbl 0562.35001

P.J. Huber, Robust Estimation of a Location Parameter, Ann. Math. Statist., 1964, Vol. 35, pp. 73-101. | MR 161415 | Zbl 0136.39805

P.J. Huber, Robust Statistics, Wiley, New York, 1981. | MR 606374 | Zbl 0536.62025

I.M. Johnstone, Admissible Estimation, Dirichlet Principles and Recurrence of Birth-Death Chains on Zp+, Prob. Theory and Related Fields (= Z. Wahrsch. Th.), Vol. 71, 1986, pp. 213-269. | Zbl 0592.62009

I.M. Johnstone and K.B. Macgibbon, Une mesure d'information caractérisant la loi de Poisson, Séminaire de Probabilités, Vol. XXI, 1987, pp.563-573, Lecture Notes in Mathematics, Vol. 1247, J. AZEMA, P. A. MEYER and M. YOR Eds., Springer Verlag, New York. | Numdam | MR 942005 | Zbl 0621.60028

I.M. Johnstone and K.B. Macgibbon, Minimax Estimation of a Constrained Poisson Vector, Ann. Statist., Vol. 20, 1992, pp. 807-831. | MR 1165594 | Zbl 0761.62006

O.A. Ladyzhenskaya and N.N. Ural'Tseva, Linear and Quasilinear Elliptic Equations, English translation, New York, Academic Press, 1968 (2nd. Russian edition, 1973). | MR 244627 | Zbl 0164.13002

B.Ya. Levit, On Asymptotic Minimax Estimates of the Second Order, Translation: Theor. Prob. Appl., Vol. 25, 1980, pp. 552-568. | Zbl 0494.62035

B.Ya. Levit, Minimax Estimation and Positive Solutions of Elliptic Equations, Translation: Theor. Prob. Appl., Vol. 27, 1982, pp. 563-586. | MR 673924 | Zbl 0518.62031

B.Ya. Levit, Second Order Asymptotic Optimality and Positive Solutions of Schrödinger's Equation, Translation: Theor. Prob. Appl., Vol. 30, 1985 a, pp. 333-363. | MR 792622 | Zbl 0608.62035

B.Ya. Levit, Evaluation of the Minimax Risk, Fourth International Vilnius Conf. Prob. Theory Math. Stat., Vol. 4, Vilnius, 1985 b, pp.181-183.

B.Ya. Levit, On Second Order Admissibility in Simultaneous Estimation, Proc. 1st World Congress Bernouilli Soc. Tashkent, U.S.S.R., 1986, Yu. A. PROHOROV and V. V. SAZONOV Eds., V.N.U. Sc. Press, Utrecht. | MR 1092458 | Zbl 0686.62017

M. Loève, Probability Theory I, Springer Verlag, New York, 1977. | MR 651017 | Zbl 0359.60001

A.A. Melkman and Y. Ritov, Minimax Estimation of the Mean of a General Distribution when the Parameter Space is Restricted, Ann. Statist., Vol. 15, 1987, pp. 432-442. | MR 885749 | Zbl 0621.62030

C. Miranda, Partial Differential Equations of Elliptic Type, 2nd. ed., Springer Verlag, New York, Heidelberg, 1970. | MR 284700 | Zbl 0198.14101

J.M. Steele, Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process, Ann. Prob., Vol. 14, 1986, pp. 326-335. | MR 815974 | Zbl 0592.60033