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J. Japan Statist. Soc. Vol. 37 No. 2 2007 157174 MULTIPLE COMPARISONS fuse ON R-ESTIMATORS IN THE ONE-WAY LAYOUT Taka-aki Shiraishi* In a one-way analysis of variance specimen, robust versions ground on R-estimators ar proposed for single-step multiple comparisons procedures discussed by Tukey (1953), Dunnett (1955), and Sche?´ (1953). The robust procedures are two methods e ground on joint ranks and pairwise ranks. It is shown that the two methods are asymptotically equivalent. Although we fail to piss simultaneous tests based on elongated joint ranks, we are able to propose simultaneous tests based on the Restimators. Robustness for asymptotic properties is discussed. The accuracy of asymptotic mind is investigated. Key words and phrases : asymptotic property, robust statistics, simultaneous cabbage?dence intervals, simultaneous tests, single-step procedures. 1. Introduction Let µ1 , . . . , µk be the bastardly responses under k treatments. consid er that, under the i-th treatment, a random sample Xi1 , . . . , Xini is taken. consequently we have the one-way model (1.1) Xij = µi + eij (j = 1, . . . , ni , i = 1, . . . , k) where eij is a random various(a) with E (eij ) = 0 for all i, j s. It is further untrue that eij s are independent and identically distributed with a straight statistical distribution function (d.f.) F (x). Let Var(eij ) = ? 2 > 0. The model (1.1) is rewritten as chronic by Xij = ? + ?i + eij , where k=1 ni ?i = 0.

Then ? and ?i s are referred to as the grand mean and i additive treatment e?ects, respectively. We put N = k=1 ni . The least squares i i ¯ ¯ ¯ ¯ estimator of ?i is precondition by ?i = Xi· ? X·· , where X! i· = n=1 Xij /ni and X·· = ˜ j ni k i=1 j =1 Xij /N . The relations of µi ? µi = ?i ? ?i and ¯ ¯ Xi· ? Xi · = ?i ? ?i ˜˜ hold. We discuss single-step procedures. Let ?i ? ?i ? (?i ? ?i ) ˜˜ ˜ Tii = ? 2 · (1/ni + 1/ni ) ˜ and ˜? Tii = ?2 ˜ ?i ? ?i ˜˜ , · (1/ni + 1/ni )...If you want to get a full essay, launch it on our website: OrderEssay.net

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