Abstract
A class of Kolmogorov-Smirnov and Cramer-von Mises type statistics for testing symmetry about an unknown value is described. These statistics are not distribution-free, however, and, indeed, are not readily amenable to calculation. A linear rank statistic analog of the first component of the Cramer-von Mises type statistic is investigated. Asymptotic non-null properties of these procedures in the normal case are studied, and an efficiency comparison of the Cramer-vonMises statistic, the linear rank statistic analog, the modified Wil-coxon statistic, and the likelihood ratio test is reported.
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