Asymptotic Properties of Generalized Multivariate Rank Statistics

Abstract

This article discusses generalization of the well-known multivariate rank statistics under right-censored data case. Empirical process representation used to get the generalization. The marginal distribution functions are estimated by Kaplan–Meier estimators. Sufficient conditions for asymptotic normality of the generalized multivariate rank statistics under independently right censored data are specified. Several auxiliary results on sup-norm convergence of Kaplan–Meier estimators in randomly exhausting regions are given too.

Keywords:

• Independent censoring
• Kaplan–Meier estimator
• Linear rank statistics
• Multivariate rank statistics
• Right-censored data

Mathematics Subject Classification:

• Primary 62G20
• Secondary 62H20, 62N01

Acknowledgment

The authors are grateful to Professor Dorota Dabrowska for her very helpful remarks.