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

We consider the problem of testing a hypothesis on the qth quantile (Formula presented.) (for known (Formula presented.) and dependent on q) of the first population when independent samples are available from (Formula presented.) normal populations with a common unknown standard deviation (Formula presented.) and unknown as well as possibly unequal means μi’s ((Formula presented.)). 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. © 2023 Taylor & Francis Group, LLC.