关键词:
subset selection
type-III error
control population
probability of correct selection
simultaneous confidence intervals
摘要:
Consider k(>= 2) independent populations pi 1,...,pi(k) such that an observation from population pi(i) follows a logistic distribution with unknown location parameter mu(i) and common known scale parameter sigma(2), i = 1,...,k. Let mu([1]) <= ... <= mu([k]) be the unknown ordered values of its and the population associated with mu([k]), be the upper extreme population (UEP) and the population associated mu([1]) be the lower extreme population (LEP). In this paper, we discuss a procedure on the lines of Liu [On a multiple three-decision procedure for comparing several treatments with a control. Austral. J. Statist. 39, 79-97] and Boher [Multiple three-decision rules for parametric signs. J. Amer. Statist. Assoc. 74, 432-437], for classifying k logistic populations by the location parameters as better or worse than a control/standard population. In the absence of any standard/control population, we propose a selection procedure for simultaneous selection of two non-empty random size subsets, one containing population associated with largest mean and the other containing population associated with smallest mean with a pre-specified probability P* (1/k(k-1) < P* < 1). The required selection constants to implement the proposed procedures are tabulated. Using these selection constants, the simultaneous confidence intervals for the parameters mu([i])-mu([1]), i = 2,...,k, mu([k])-mu([i]), i = 1,...,k-1, are constructed. A simple instructive numerical example is given. (c) 2006 Elsevier B.V. All rights reserved.