为了检验未知总体的对称点,建立了非均等排序集抽样下的Wilcoxon符号秩检验统计量,证明了在原假设下其分布具有对称性和适应任意分布性,证明了新检验统计量的渐近正态性,并给出新检验的Pitman效率因子.Pitman渐近相对效率的计算结果表明,新检验优于简单随机抽样下和均等排序集抽样下的符号秩检验.
In order to test the symmetric point of an infinite population, a Wilcoxon signed-rank test statistic based on ranked set sampling with unequal samples is constructed. Its distribution is shown to be symmetric and distribution-free under null hypothesis. The asymptotic normality of the new test statistic is proved, and its Pitman efficiency factor is given. The calculated results of Pitman asymptotic relative efficiencies show that the new test is superior to the signed-rank tests under simple random sampling and ranked set sampling.
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