Adjusted Versus Conditional Likelihood: Power Properties and Bartlett-Type Adjustment

Abstract

SUMMARY Under contiguous alternatives the adjusted likelihood ratio (ALR) test is seen to have the same power properties as the conditional likelihood ratio test up to the third order of comparison. In particular, an optimum property of the ALR test in terms of second-order local maximinity follows. It is also seen that the ALR statistic admits a Bartlett-type adjustment.