Increasing power of the test through pre-test - a robust method

TL;DR

This paper introduces a robust pre-test procedure to improve the power of tests for the intercept in regression models when the slope is suspected to have a specific value, using M-estimation.

Contribution

It develops a pre-test testing method that asymptotically outperforms traditional tests in power, based on M-estimation techniques.

Findings

Pre-test test (PTT) shows asymptotic dominance over UT and RT.

Analytical and graphical power comparisons demonstrate PTT's effectiveness.

The method is robust and applicable when slope suspicion is present.

Abstract

This paper develops robust test procedures for testing the intercept of a simple regression model when it is \textit{apriori} suspected that the slope has a specified value. Defining unrestricted test (UT), restricted test (RT) and pre-test test (PTT) corresponding to the unrestricted (UE), restricted (RE), and preliminary test estimators (PTE) in the estimation case, the M-estimation methodology is used to formulate the M-tests and derive their asymptotic power functions. Analytical and graphical comparisons of the three tests are obtained by studying the power functions with respect to size and power of the tests. It is shown that PTT achieves a reasonable dominance over the others asymptotically.