Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 2, 186-198

A SMALL AND LARGE SAMPLE COMPARISON OF WALD'S LIKELIHOOD RATIO AND RAO'S TESTS FOR TESTING LINEAR REGRESSION WITH AUTOCORRELATED ERRORS

By

BRAJENDRA C. SUTRADHAR,

And

ROY F. BARTLETT, *Memorial University of Newfoundland*

SUMMARY. This paper, through a simulation study, examines the behaviour of Wald's, likelihood ratio and Rao's tests for testing a linear regression model with autocorrelated errors. The tests were performed at the standard 5% level of significance (size) and it was found that for negative and moderate positive autocorrelations of first order, the likelihood ratio and Wald's tests lead to inflated significance levels in general, and Rao's test is conservative. For large positive autocorrelations, the performance of these tests is worse even when the sample size is large, the likelihood ratio and Wald's tests being highly liberal and Rao's test being highly conservative. For various local alternatives, a comparison of power is given after empirically modifying the original test procedures so that all these tests have the same (5%) size. It is found that Rao's size adjusted test is uniformly more powerful than the size-adjusted likelihood ratio and size-adjusted Wald's tests.

*AMS (1980) subject classification.* 62G10, 62E25

*Key words and phrases*. Multi-dimensional composite hypothesis, Monte Carlo study, autocorrelated errors, power of the size-adjusted tests