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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 32, Fasc. 2,
pages 301 - 322
 

DATA DRIVEN SCORE TESTS FOR UNIVARIATE SYMMETRY BASED ON NON-SMOOTH FUNCTIONS

Jadwiga Józefczyk

Abstract: We propose data driven score rank tests for univariate symmetry around a known center based on non-smooth functions. A choice of non-smooth functions is motivated by very special properties of a certain function on [0,1] determined by a distribution which is responsible for its asymmetry. We modify recently introduced data driven penalty selection rules and apply Schwarz-type penalty as well. We prove basic asymptotic results for the test statistics. In a simulation study we compare the empirical behavior of the new tests with the data driven tests based on the Legendre basis and with the so-called hybrid test. We show good power behavior of the new tests often overcoming their competitors.

2000 AMS Mathematics Subject Classification: Primary: 62G10; Secondary: 65C05, 62G99.

Keywords and phrases: Testing symmetry, data driven score test, rank test, selection rule, hybrid test, Monte Carlo study.

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