Testing on the Quantiles of a Single Normal Population in the Presence of Several Normal Populations with a Common Variance

Abstract

We consider the problem of testing a hypothesis on the qth quantile ${\xi }_q=\xi (\text{say})={\mu }_1+\nu \sigma$ (for known $\nu \ne 0,$ and dependent on q) of the first population when independent samples are available from $k(\ge 2)$ normal populations with a common unknown standard deviation $\sigma ,$ and unknown as well as possibly unequal means μi’s ($1\le i\le k$). We discuss several test methods, such as the ones based on the computational approach test (CAT), the asymptotic likelihood ratio test (ALRT), the parametric bootstrap likelihood ratio test (PBLRT), and tests based on the generalized p value approach. The performance of these tests, in terms of size and power, have been studied through a comprehensive simulation study, and recommendations have been made about their applicability. Finally, usage of these tests have demonstrated by using three real-life datasets.

KEYWORDS AND PHRASES:

• Asymptotic likelihood ratio test (ALRT)
• computational approach test (CAT)
• generalized p value method
• parametric bootstrap likelihood ratio test (PBLRT)
• power/size comparison

Acknowledgment

The authors would like to sincerely thank the anonymous reviewers and the editor-in-chief for their valuable suggestions and comments, which helped to improve the presentation of the work.

Disclosure Statement

No potential conflict of interest was reported by the author(s).