Empirical distributions of the robustified $t$-test statistics

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.