On Nonparametric Maximum Likelihood Estimations of Multivariate Distribution Function Based on Interval-Censored Data

Abstract

This article considers the nonparametric maximum likelihood estimator (NPMLE) of a joint distribution function when the multivariate failure times of interest are interval-censored. With different types of interval censoring mechanism, the NPMLE's of the multivariate distribution function are studied and the strong consistency for the NPMLEs is obtained in terms of a self-consistency equation. Furthermore, the convergence rate of the estimator is given, which depends on the types of interval censoring mechanism.

Keywords:

• Convergence rate
• Self-consistency equation
• Strong consistency

Mathematics Subject Classification:

• Primary 62G20, 62N01
• Secondary 62G05

Acknowledgments

This work is partly supported by a grant from the Natural Science and Engineering Research Council of Canada. Authors are very grateful to the referees for their comments and suggestions.