Nonparametric Tests of Homogeneity Against Restricted Alternatives in a One-Way Classification.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK ORDNANCE RESEARCH LAB
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The Chernoff-Savage Theorem is extended to prove that the c2 dimensional vector of Chernoff Savage two-sample statistics computed among samples from c populations and statistics in the class L of linear combinations of the c2 two-sample statistics are asymptotically normally distributed. A sub-class L of L consisting of linear combinations of c-1 two-sample statistics computed using adjacent samples under an ordered alternative is studied. Each statistic T epsilon L has an equivalent statistic T epsilon L. For testing homogeneity of location against ordered alternatives, the Pitman and Bahadur approximate efficiencies of T with respect to T are one and greater than one, respectively, while T is computationally simpler than T. However, for very small sample sizes, the variance of T under HO may be greater than that of T, possibly offsetting the increased Bahadur efficiency. If the ordered alternative is further restricted by specifying the relative spacing in the alternative, the statistic in L having maximum Pitman efficiency is obtained. It is proved that the statistics in L proposed by Jonckheere and Puri have maximum Pitman efficiency for equal spacings. Author
- Statistics and Probability