Empirical distributions of the robustified $t$-test statistics

TL;DR

This paper investigates the empirical distributions of robustified $t$-test statistics based on median and median absolute deviation estimators, providing practical quantile values for small sample inference through extensive simulations.

Contribution

It offers empirical distributions and quantile values for robustified $t$-tests, improving small sample inference where asymptotic results are inadequate.

Findings

Empirical distributions differ from asymptotic ones for small samples.

Quantile tables enable more accurate hypothesis testing.

Robustified $t$-tests improve inference robustness.

Abstract

Based on the median and the median absolute deviation estimators, and the Hodges-Lehmann and Shamos estimators, robustified analogues of the conventional $t$-test statistic are proposed. The asymptotic distributions of these statistics are recently provided. However, when the sample size is small, it is not appropriate to use the asymptotic distribution of the robustified $t$-test statistics for making a statistical inference including hypothesis testing, confidence interval, p-value, etc. In this article, through extensive Monte Carlo simulations, we obtain the empirical distributions of the robustified $t$-test statistics and their quantile values. Then these quantile values can be used for making a statistical inference.