Inefficient estimators of the bivariate survival function for three models
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 3, pp. 545-597.
@article{AIHPB_1995__31_3_545_0,
     author = {Gill, Richard D. and Laan, Mark J. van der and Wellner, Jon A.},
     title = {Inefficient estimators of the bivariate survival function for three models},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {545--597},
     publisher = {Gauthier-Villars},
     volume = {31},
     number = {3},
     year = {1995},
     mrnumber = {1338452},
     zbl = {0855.62024},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1995__31_3_545_0/}
}
TY  - JOUR
AU  - Gill, Richard D.
AU  - Laan, Mark J. van der
AU  - Wellner, Jon A.
TI  - Inefficient estimators of the bivariate survival function for three models
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1995
SP  - 545
EP  - 597
VL  - 31
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1995__31_3_545_0/
LA  - en
ID  - AIHPB_1995__31_3_545_0
ER  - 
%0 Journal Article
%A Gill, Richard D.
%A Laan, Mark J. van der
%A Wellner, Jon A.
%T Inefficient estimators of the bivariate survival function for three models
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1995
%P 545-597
%V 31
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1995__31_3_545_0/
%G en
%F AIHPB_1995__31_3_545_0
Gill, Richard D.; Laan, Mark J. van der; Wellner, Jon A. Inefficient estimators of the bivariate survival function for three models. Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 3, pp. 545-597. http://www.numdam.org/item/AIHPB_1995__31_3_545_0/

P.K. Andersen, Ø. Borgan, R.D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag, New York, 1992. | Zbl

D.M. Bakker, Two nonparametric estimators of the survival function of bivariate right censored observations, Report BS-R9035, Centre for mathematics and computer science, Amsterdam, 1990.

P.J. Bickel, Y. Ritov and J.A. Wellner, Efficient estimation of linear functionals of a probability measure P with known marginal distributions, Ann. Statist., Vol. 19, 1991, pp. 1316-1346. | MR | Zbl

P.J. Bickel, C.A.J. Klaassen, Y. Ritov and J.A. Wellner, Efficient and Adaptive Estimation for Semiparametric Models, John Hopkins University Press, 1993. | MR | Zbl

M.D. Burke, Estimation of a bivariate survival function under random censorship, Biometrika, Vol. 75, 1988, pp. 379-382. | MR | Zbl

D.M. Dabrowska, Kaplan Meier Estimate on the Plane, Ann. Statist., Vol. 16, 1988, pp. 1475-1489. | MR | Zbl

D.M. Dabrowska, Kaplan Meier Estimate on the Plane: Weak Convergence, LIL, and the Bootstrap, J. Multivar. Anal., Vol. 29, 1989, pp. 308-325. | MR | Zbl

R.M. Dudley, Weak convergence of probabilities on nonseparable metric spaces, and empirical measures on Euclidean spaces, Illinois J. Math., Vol. 10, 1966, pp. 109-126. | MR | Zbl

R.M. Dudley, Fréchet differentiability, p-variation and universal Donsker classes. Ann. Prob. Vol. 20, 1991, pp. 1968-1983. | MR | Zbl

R.M. Dudley, Empirical processes, p-variation for p ≤ 2 and the quantile and ∫ FdG operator, unpublished manuscript 1992.

R.D. Gill, Non- and Semi-parametric Maximum Likelihood Estimators and the von Mises Method (Part 1), Scand. J. Statist., Vol. 16, 1989, pp. 97-128. | MR | Zbl

R.D. Gill and S. Johansen, A survey of product integration with a view towards application in survival analysis, Ann. Statist., Vol. 18, 1990, pp. 1501-1555. | MR | Zbl

R.D. Gill, Multivariate survival analysis, Theory Prob. Appl., Vol. 37, 1992, pp. 18-31 and 307-328 (in Russian; English translation to appear). | Zbl

E. Giné and J. Zinn, Bootstrapping general empirical measures, Ann. Probability, Vol. 18, 1990, pp. 284-301. | MR | Zbl

J. Hoffmann-Jørgensen, Stochastic Processes on Polish Spaces, unpublished manuscript, 1984.

L.V. Kantorovich and G.P. Akilov, Functional Analysis, translated by Howard L. Silcock, New York, Permagon Press, 1982. | MR | Zbl

M.J. Van Der Laan, Dabrowska's multivariate product limit estimator and the delta-method, Master's Thesis, Dept. of Math., Utrecht Univ., 1990.

M.J. Van Der Laan, Analysis of Pruitt's estimator of the bivariate survival function, preprint No. 648, Dept of Math., Utrecht Univ., 1991.

M.J. Van Der Laan, Efficient Estimator of the Bivariate Survival Function for Right Censored Data, Technical Report No. 337, Department of Statistics, University of California, Berkeley, 1992.

M. Loève, Probability Theory, van Nostrand, New York, 1955. | MR | Zbl

G. Neuhaus, On weak convergence of stochastic processes with multidimensional time parameter, Ann. Math. Statist., Vol. 42, 1971, pp. 1285-1295. | MR | Zbl

D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984. | MR | Zbl

R.L. Prentice and J. Cai, Covariance and survivor function estimation using censored multivariate failure time data, Biometrika, Vol. 79, 1992a, pp. 495-512. | MR | Zbl

R.L. Prentice and J. Cai, Marginal and conditional models for the analysis of multivariate failure time data. Klein J. P. and Goel P. K., Eds., Survival Analysis State of the Art, Kluwer, Dordrecht, 1992b. | Zbl

R.C. Pruitt, On negative mass assigned by the bivariate Kaplan-Meier estimator, Ann. Stat., Vol. 19, 1991a, pp. 443-453. | MR | Zbl

R.C. Pruitt, Small sample comparisons of five bivariate survival curve estimators, Technical Report No. 559, University of Minnesota, 1991a.

R.C. Pruitt, Strong consistency of self-consistent estimators: general theory and an application to bivariate survival analysis, Technical Report No. 543, University of Minnesota, 1991b.

J.A. Reeds, On the definition of von Mises functionals, Ph. D. thesis, Dept. of Statistics, Harvard University, Research Report S-44, 1976.

A. Sheehy and J.A. Wellner, Uniformity in P of some limit theorems for empirical measures and processes, Technical Report No. 134, Dept. of Statistics, Univ. of Washington, 1988.

A. Sheehy and J.A. Wellner, Uniform Donsker Classes of Functions, Ann. Probability, Vol. 20, 1992, pp. 1983-2030. | MR | Zbl

G.R. Shorack and J.A. Wellner, Empirical Processes. Wiley, New York, 1986. | MR

A.W. Van Der Vaart and J.A. Wellner, Prohorov and continuous mapping theorems in the Hoffmann-Jørgensen weak convergence theory, with application to convolution and asymptotic minimax theorems, Tech. Report No. 157. Dept. of Statistics, University of Washington, Seattle, 1989.

A.W. Van Der Vaart and J.A. Wellner, Weak Convergence and Empirical Processes, Springer Verlag, New York, to appear 1995. | MR | Zbl

J.A. Wellner, Covariance formulas via marginal martingales, Statistica Neerlandica, Vol. 48, 1994. | MR | Zbl