Comparison of Efficiencies of Symmetry Tests around Unknown Center

TL;DR

This paper compares the efficiency of various symmetry tests around an unknown center, using asymptotic analysis and Bahadur efficiency, with modifications based on an estimated center.

Contribution

It introduces modified symmetry tests using an alpha-trimmed mean estimator and analyzes their asymptotic behavior and efficiency.

Findings

Modified tests are asymptotically valid.

Some tests show higher Bahadur efficiency.

Comparison highlights the most effective symmetry tests.

Abstract

In this paper, some recent and classical tests of symmetry are modified for the case of an unknown center. The unknown center is estimated with its $\alpha$-trimmed mean estimator. The asymptotic behavior of the new tests is explored. The local approximate Bahadur efficiency is used to compare the tests to each other as well as to some other tests.