ESTIMATION IN A STATISTICAL CONTROL PROBLEM

LLOYD MARK BERLINER, Purdue University

Abstract

Let X have a p-variate normal distribution with unknown mean (theta) and identity covariance matrix. The problem is to choose a decision rule (delta)(X) subject to incurring a loss L((delta),(theta)) = ((theta)('t)(delta)-1)('2). This decision problem is shown to be a transformed version of a control problem in which control levels are to be chosen in a linear model so that the resulting dependent random variable is close to a desired value. The admissibility of spherically symmetric generalized Bayes rules is considered. Such rules are shown to be admissible under certain conditions on their corresponding prior densities. The essential condition is that the density be bounded by K (VBAR)(theta)(VBAR) ('(4-p)) for (VBAR)(theta)(VBAR) large. A general technique for comparing decision rules in terms of risk is introduced. Application of this technique yields results useful in investigating inadmissibility. Classes of rules which dominate standard inadmissible rules are presented. The minimaxity of classes of rules is investigated. New rules are derived and evaluated by decision theoretic criteria.

Degree

Ph.D.

Subject Area

Statistics

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