Danish

J. Japan Statist. Soc. Vol. 37 no 2 2007 157174 MULTIPLE COMPARISONS lay down ON R-ESTIMATORS IN THE unidirectional LAYOUT Taka-aki Shiraishi* In a unidirectional analysis of variance mildew, fat versions ground on R-estimators ar proposed for single-step multiple comparisons procedures discussed by Tukey (1953), Dunnett (1955), and Sche?´ (1953). The spicy procedures are 2 methods e found on joint ranks and pairwise ranks. It is shown that the two methods are asymptotic on the wholey equivalent. Although we fail to defecate simultaneous tests establish on analog joint ranks, we are adequate to(p) to propose simultaneous tests based on the Restimators. Robustness for asymptotic properties is discussed. The accuracy of asymptotic appraisal 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 discussions. press that, under the i-th treatment, a haphazard 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 versatile with E (eij ) = 0 for all i, j s. It is further assumed that eij s are independent and identically distributed with a continuous 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 reverend 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 Xi· = n=1 Xij /ni and X·· = ˜ j ni k i=1 j =1 Xij /N . The traffic 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 pose a full essay, commit it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper