Title: Empirical distributions of the robustified $t$-test statistics,
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.