The Exact Finite Sample Distribution of Theil's Compatibility Test Statistic and its Application

Abstract

In this article we derive the exact finite sample distribution of a statistic utilized by Theil [10] to test whether sample and prior information are in conflict with each other. A weighted estimator for the slope coefficient in a simple regression equation with one independent variable is obtained by using weights which are determined by the observed value of Theil's test statistic. This weighted estimator is particularly useful when we are uncertain about the compatibility of prior information with sample information.