Test for intercept after pre-testing on slope - a robust method

Abstract

The idea of using non-sample prior information in the form of pre-testing for improving properties of estimators is applied in the testing regime to achieve better power of the ultimate test in this paper. In particular, to test the intercept of a simple regression model, prior information from previous investigations or expert knowledge on the suspected value of the slope is potentially benefcial. Any uncertainty on the value of the slope is removed by performing a pre-test before testing the signicance of the intercept. The impact of the pre-test on the performance (power and size) of the ultimate test is studied. A robust procedure based on M-estimator is used to formulate a test and deriving its power function. It is shown that the ultimate test based pre-test achieves a reasonable dominance over the others asymptotically and performs better for larger coefcient of variation.