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J. Japan Statist. Soc. Vol. 37 No. 2 2007 157174 MULTIPLE COMPARISONS background knowledge ON R-ESTIMATORS IN THE ONE-WAY LAYOUT Taka-aki Shiraishi* In a unidirectional analysis of variance moulding, 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 found 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 analog joint ranks, we are able to propose simultaneous tests based on the Restimators. Robustness for asymptotic properties is discussed. The accuracy of asymptotic idea is investigated. Key words and phrases : asymptotic property, robust statistics, simultaneous determine?dence intervals, simultaneous tests, single-step procedures. 1. Introduction Let µ1 , . . . , µk be the bastardly responses under k treatments. consider 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 with E (eij ) = 0 for all i, j s. It is further fictive that eij s are independent and identically distributed with a invariable 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 bilinear 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 Xi· = 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, put in it on our website: BestEssayCheap.com

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