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Inefficient estimators of the bivariate survival function for three models. (English) Zbl 0855.62024

Summary: Three explicit estimators of the bivariate survival functions for three types of data are analyzed by proving the analytical and probabilistic conditions necessary for application of the functional delta-method. It tells us that the estimators converge weakly at \(\sqrt n\)-rate to a Gaussian process and that for estimation of their asymptotical distribution the bootstrap works well. We also prove efficiency of the Dabrowska and Prentice-Cai estimators [D. M. Dabrowska, Ann. Stat. 16, No. 4, 1475-1459 (1988; Zbl 0653.62071); J. Multivariate Anal. 29, No. 2, 308-325 (1989; Zbl 0667.62025); R. L. Prentice and J. Cai, Biometrika 79, No. 3, 495-512 (1992; Zbl 0764.62095)] for the bivariate censoring model under independence.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
62G09 Nonparametric statistical resampling methods
60F17 Functional limit theorems; invariance principles
62G07 Density estimation
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