The Asymptotic Distribution of Conditional Likelihood Ratio Tests

Abstract

A conditional likelihood ratio test for testing a hypothesis concerning structural parameters in the presence of infinitely many incidental parameters is suggested. It is shown that the usual X² approximation to the log-likelihood ratio fails to work in many situations involving incidental parameters. In contrast it is shown that the X² approximation can be used in large samples under fairly general assumptions if we use conditional likelihood ratio tests instead. The relationship between the theory of UMPU-test and conditional likelihood ratio tests is discussed, and some examples are given to show that the conditional likelihood ratio approach covers more cases than the UMPU approach.