AN EXTENSION OF THE CONDITIONAL LIKELIHOOD RATIO TEST TO THE GENERAL MULTIPARAMETER CASE

RAHUL MUKERJEE

Indian Institute of Management, Joka, Diamond Harbour Road, Post Box No. 16757, Alipore Post Office, Calcutta 700 027, India

(Received February 12, 1992; revised December 22, 1992)

Abstract. In a set-up, where both the interest parameter and the nuisance parameter are possibly multi-dimensional and global parametric orthogonality may not hold, we suggest a test that is superior to the usual likelihood ratio test with regard to second-order local maximinity. The test can be motivated from the principles of conditional and adjusted likelihood.

Key words and phrases: Adjusted likelihood, conditional likelihood, contiguous alternative, local maximinity, parametric orthogonality, power, second order.