A Nonparametric Test Procedure Based on Quantiles for the Right Censored Data

Abstract

In this study, we propose nonparametric tests using the several quantile statistics simultaneously for the right censored data. First of all, we consider statistics of the quadratic form with estimated covariance matrices. Then we derive the limiting distribution using the large sample approximation theory. Also we consider different forms of statistics such as the maximal and summing types with their limiting distributions. Then we illustrate our procedure with examples and compare performance among tests with empirical powers through a simulation study. Also we comment briefly on some interesting features including re-sampling methods as concluding remarks. Finally in Appendices, we provide proofs for the theoretic results needed for the derivation of the limiting distributions of the proposed test statistics.

Keywords:

• Bahadur-type representation
• Kaplan–Meier estimate
• Nonparametric test
• Quantile test
• Right censored data

Mathematics Subject Classification:

• 62N03
• 62G10

Acknowledgment

The author would like to express his sincere appreciation to two anonymous referees for pointing out errors and suggesting constructive advices.