A Nonparametric Procedure for Choosing a Location Test

Abstract

This paper studies a procedure for choosing a location test based on estimated asymptotic powers. The estimation of the power uses the bootstrap. At present, practicians often exclusively use the t-test. The procedure proposed in this paper can-depending on the underlying population-lead to a test having much higher power than the t-test.

The paper discusses in detail a “black box” which contains two different tests, the t-test and a robust test based on an Mestimator. Given a sample x ₁, …, x _n, the “black box” estimates the asymptotic power of the two tests and then applies the seemingly more powerfull. This procedure is studied via simulations which (1) show the quality of the power estimates and (2) compare the power of the “black box” with the power of the t-test and the robust test.

Keywords:

• bootstrap
• asymptotic power
• simulated power