Increasing the Power of the Test Through Pre-Test – A Robust Method

Abstract

Robust test procedures are developed for testing the intercept of a simple regression model when the slope is (i) completely unspecified, (ii) specified to a fixed value, or (iii) suspected to be a fixed value. Defining (i) unrestricted (UT), (ii) restricted (RT), and (iii) pre-test test (PTT) functions for the intercept parameter under the three choices of the slope, tests are formulated using the M-estimation methodology. The asymptotic distributions of the test statistics and their asymptotic power functions are derived. The analytical and graphical comparisons of the tests reveal that the PTT achieves a reasonable dominance over the other tests.

Keywords:

• Asymptotic size
• Asymptotic power
• Contiguity
• M-estimation
• Pre-test
• Regression model

Mathematics Subject Classification:

• Primary 62G10, 62G35
• Secondary 62G20

Acknowledgments

The authors gratefully acknowledge the valuable suggestions of Professor A K Md E Saleh, Carleton University, Canada that helped improve the content and quality of the results in the paper. Some useful suggestions by an unknown referee are also acknowledged.