On the limiting Pitman efficiency of some rank tests of independence
Kendall's tau and Spearman's rho may be expressed by the use of standard sequences with parameter \(a=1\). The paper uses the fact that the main assumption of \textit{H. S. Wieand}'s theorem [Ann. Stat. 4, 1003-1011 (1976; Zbl 0351.62033)] may be replaced by an equivalent one which is presented in section 2. Taking \(R_ i(S_ i)\) as the rank of \(X_ i(Y_ i)\) and I(A) as the indicator of the set A, the statistic \[ t_ n=\sup_{0<p<1}(12n)^{1/2}(\sum^{n}_{i=1}(R_ i/n)(p-I(S_ i\leq np))/n) \] is also usable for testing independence and it is a standard sequence with \(a=4\). Section 3 is devoted to prove that \(t_ n\) fulfills the equivalent condition as Kendall's tau and Spearman's rho do. Then the well known theorem of \textit{J. Kiefer} and \textit{J. Wolfowitz} [Trans. Am. Math. Soc. 87, 173-186 (1958; Zbl 0088.113)] is satisfied. Some examples of the limiting Pitman efficiency of the statistics studied are derived in Section 4.
scientific article; zbMATH DE number 3996880
scientific article