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 , p. 545-597
Zbl 0855.62024 | MR 1338452
URL stable :


P.K. Andersen, Ø. Borgan, R.D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag, New York, 1992. Zbl 0824.60003

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 1126327 | Zbl 0742.62034

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 1245941 | Zbl 0786.62001

M.D. Burke, Estimation of a bivariate survival function under random censorship, Biometrika, Vol. 75, 1988, pp. 379-382. MR 946057 | Zbl 0641.62028

D.M. Dabrowska, Kaplan Meier Estimate on the Plane, Ann. Statist., Vol. 16, 1988, pp. 1475-1489. MR 964934 | Zbl 0653.62071

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 1004341 | Zbl 0667.62025

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 185641 | Zbl 0178.52502

R.M. Dudley, Fréchet differentiability, p-variation and universal Donsker classes. Ann. Prob. Vol. 20, 1991, pp. 1968-1983. MR 1188050 | Zbl 0778.60026

R.M. Dudley, Empirical processes, p-variation for p ≤ 2 and the quantile and ∫ FdG operator, unpublished manuscript 1992.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 1028971 | Zbl 0688.62026

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 1074422 | Zbl 0718.60087

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 0780.62086

E. Giné and J. Zinn, Bootstrapping general empirical measures, Ann. Probability, Vol. 18, 1990, pp. 284-301. MR 1055437 | Zbl 0706.62017

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 664597 | Zbl 0484.46003

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 203748 | Zbl 0066.10903

G. Neuhaus, On weak convergence of stochastic processes with multidimensional time parameter, Ann. Math. Statist., Vol. 42, 1971, pp. 1285-1295. MR 293706 | Zbl 0222.60013

D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984. MR 762984 | Zbl 0544.60045

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 1187604 | Zbl 0764.62095

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 0850.62846

R.C. Pruitt, On negative mass assigned by the bivariate Kaplan-Meier estimator, Ann. Stat., Vol. 19, 1991a, pp. 443-453. MR 1091861 | Zbl 0738.62049

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 1188051 | Zbl 0763.60012

G.R. Shorack and J.A. Wellner, Empirical Processes. Wiley, New York, 1986. MR 838963

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 1385671 | Zbl 0862.60002

J.A. Wellner, Covariance formulas via marginal martingales, Statistica Neerlandica, Vol. 48, 1994. MR 1310337 | Zbl 0829.62097