(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.