AISM 54, 382-390

© 2002 ISM

## Asymptotic efficiency of Maesono statistics for testing of symmetry

### Ya. Yu. Nikitin and E.V. Ponikarov

Department of Mathematics and Mechanics, St. Petersburg State
University, 198504 Petrodvorets, Russian Federation

(Received April 4, 2000; revised December 25, 2000)

Abstract.
In an interesting paper Maesono introduced a new class of distribution-free statistics
for testing of symmetry against shift alternative. The simplest of them coincides with the Wilcoxon statistic while the next is different but has the same Pitman efficiency. Maesono raised the problem of comparison between these two statistics on the basis of
*exact* Bahadur efficiency. In this paper we calculate exact
local Bahadur indices for all Maesono statistics and show when his
statistics are better than the Wilcoxon statistic for sufficiently
close alternatives.

Key words and phrases:
Bahadur efficiency, large deviations, U-statistics, Wilcoxon test, exact slope, local index, Maesono statistics.

**Source**
(TeX , DVI )