On a Class of Rank Order Tests for Regression with Partially Informed Stochastic Predictors

Abstract

Hajek (1962) has obtained asymptotically most powerful rank order tests for simple linear regression with non-stochastic predictors. His findings are extended here to the multiple linear regression model with stochastic predictors, including the situations where the predictors are partially informed. The proposed tests are shown to be conditionally distribution-free. Their asymptotic properties and efficiencies are studied, and the asymptotic optimality is established under the conditions of Wald (1943).