DATA DRIVEN SCORE TESTS FOR UNIVARIATE SYMMETRY BASED ON
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 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,
Keywords and phrases: Testing symmetry, data driven score test, rank test, selection
rule, hybrid test, Monte Carlo study.