Efficiency and Optimality Properties of a Class of k-Sample Rank Tests Against Trend
نویسنده
چکیده
A class of k-sample rank tests is considered for testing the hypothesis Ho: F i (x) = F (x), i < k against the hypothesis H I : F i (x) = F (x Oi), 01 < 02 < 9 9 9 < O k, 01 4: O k. These tests are based on a rank statistic S = ~ d i (-~) ~ a n (R_i,r 3') in which -~= (nl . . . . . nk) . I fn -Xni, n -* ~i and n 1/20i , n ~ 0 i it is shown that Eff ((~, d ~, 3') I (F, b-')) = Eff (~ IF) Eff (~ 7) Eff~ (b*l b*). For given ~ the 'minimax' efficiency weight-vector do (~) is derived with respect to | = (O'1 -1 = O 1 < . . . ~< Ok = 1 ) and also the Bayes vector ff(~, r) with respect to a d.f. r on e . The properties of these tests are investigated. Further an allied class of tests is considered based on a statistic W = ~ ~ d . . (n ~) W_h,i, where _W h i is a rank statistic for the samples taken o f x h and x .. h < i n , t , t
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