LOCALLY MOST POWERFUL RANK TESTS FOR INDEPENDENCE

概要

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In testing independence of two random variables based on rank statistics, several rank statistics such as Spearman's $ \rho $, Kendall's $ \tau $, normal score statistics, etc. are available and performance of the tests based on these statistics has been studied for some models ; see, e. g., Bhuchongkul [3], Farlie [5], Hajek and Sidak [8] and Konijn [9]. In this paper we study the one-sided and two-sided locally most powerful rank tests (LMPRT) to test the independence of $ p $-dimensional random variables $ (p \geqq 2) $ with $ q $-parameters, where the independence is characterized by the value zero for all parameters. The term 'locally' means that parameters are included in some neighbourhood of the origin. Two-sided LMPRT will be considered only when onesided LMPRT does not exist. In Sections 5 and 6 a symptotic normality of the test statistic in the one-sided LMPRT will be studied. In this paper, only total independency is adopted as a null hypothesis, so that neither pairwise independence nor general independency of sets of variables will not be dealt with. These two independencies have been studied in Puri and Sen [12] and their other several papers and also in Anderson [2] for the normal case.