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

Abstract

[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 bene¯cial. 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.