Comparison of Efficiencies of Symmetry Tests around Unknown Center

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.

The final version will appear in Statistics