Multivariate One-Sided Tests for the Right Censored Data

In this paper, first of all, we formulate the one-sided alternatives for the multivariate data and propose an asymptotically nonparametric test procedure with possibly right censored observations in the spirit of Boyett, Shuster (1977). Therefore the corresponding statistics are constructed by taking the maximum among all the marginal components which are standardized. Then we consider obtaining asymptotic tail probability (or p-value) by showing that the distributions of our proposed test statistics are asymptotically related with multivariate normal ones with the large sample approximation theorem with the estimated limiting variances based on the counting process theory. Also we compare the performance of our proposed test with other procedures by obtaining empirical powers through a simulation study for the bivariate case. Then we exemplify our procedure with an example and compare the p-values of other procedures with our procedure. Finally, we discuss some interesting aspects and properties of our procedure briefly and state briefly various types of statistics which can be used for the one-sided alternatives for the multivariate data.