Some Contributions to the Theory of Incompletely Specified Models

The impact of preliminary tests on inferences in the Theory of Incompletely Specified Models

Abstract

This paper study of the situation is such that the solutions of the problem of Some Contributions to the Theory of Incompletely Specified Models are necessarily optimized by the same value of . Two sided tests of Specified Models are optimized by roughly the same value of that optimizes the estimation problem. However, tests of Specified Models need not have this property. It appears that recommendations for selecting the level of significance of the preliminary test depend upon the type of inferences on θ one is desirous of making. The problem to be analyzed here is that of using a preliminary test to determine whether a one parameter or a two parameter exponential distribution should be assumed as the Theory of Incompletely Specified Models for subsequent inferences and how this decision affects the properties of such inferences. It is a well-known fact that if one makes a test of theory using the same set of data used in performing some preliminary test, the power and size of that test are generally different from the power and size of a test made independently of any preliminary test for Specified Models.