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.


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
Full Text: Numdam EuDML