Characterizations of symmetry via central order statistics and the applications to goodness-of-fit testing

Abstract

In recent times, goodness-of-fit tests based on characterizations have become very popular. In case of symmetry testing, this approach is not much explored. We present some recent characterizations of symmetry around zero that use some properties of the order statistics, as well as some new classes of symmetry tests based on those characterizations . For measuring the quality of those tests we calculate their asymptotic efficiencies against some common alternatives and compare them with other symmetry tests. We also suggest some modifications of the proposed tests, so they could be applied in case of testing symmetry around unknown location. The power comparison for small sample sizes and some applications will also be presented.