# Smoothed nonparametric two-sample tests

## TL;DR

This paper introduces smoothed versions of the median and Wilcoxon's rank sum tests that address significance probability issues in discrete nonparametric tests, maintaining their desirable properties.

## Contribution

The paper develops new smoothed nonparametric two-sample tests that are free from significance probability problems inherent in traditional discrete tests.

## Key findings

- Smoothed tests have correct significance probabilities.
- They retain the good properties of original discrete tests.
- Theoretical analysis shows favorable local asymptotic power.

## Abstract

We propose new smoothed median and the Wilcoxon's rank sum test. As is pointed out by Maesono et al.(2016), some nonparametric discrete tests have a problem with their significance probability. Because of this problem, the selection of the median and the Wilcoxon's test can be biased too, however, we show new smoothed tests are free from the problem. Significance probabilities and local asymptotic powers of the new tests are studied, and we show that they inherit good properties of the discrete tests.