Tests for symmetry of a distribution function about an unknown value are investigated. The asymptotic distributions under symmetry as well as under near alternatives are given for two kinds of tests: trimmed Wilcoxon tests and tests based on gaps. It turns out that these procedures have a good stability of level under unimodal densities. In a special case (skewness to the left) the efficacies have been calculated. Monte Carlo results are also given.
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Antille et al. (1982) studied this question.
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