Nonparametric Estimation of a Bivariate Mean Residual Life Function

Abstract

In many statistical studies involving failure data, mean residual life function is of prime importance. The bivariate mean residual life function has received relatively less attention in the literature. In this article we use a simple nonparametric estimator for a bivariate mean residual life function. The estimator is shown to be uniformly strongly consistent and, on proper normalization, converges weakly to a zero-mean bivariate Gaussian process. Numerical studies demonstrate that the estimator performs well even for moderate sample sizes. Results are applied to a real dataset related to cancer recurrence. A few supporting results in connection with weak convergence proved in Appendix C may be of independent interest.

KEY WORDS:

• Bivariate Gaussian process
• Covering number
• Uniform strong consistency
• Vapnik-Chervonenkis class
• Weak convergence