Testing symmetry about an unknown median, via linear rank procedures

摘要: The properties of several linear rank statistics for testing the hypothesis that a random variable with unknown median has symmetric distribution, are explored. Each test is related, in natural way, to type estimator median. Specifically, tests based on swre functions which third element complete orthonormal basis L 2[O,1] and estimated by associated R-estimator. It shown linking score function this fashion resulting have simple asymptotic distribution under both null sequences local alternatives. Based theory, small sample modifications presented. n, even when approximate critical values used, these maintain stable a-level, close nominal level, over wide range distributions. Also respect power, competitive existing proc...