When is the generalized likelihood ratio test optimal?

Authors:
O. Zeitouni;J. Ziv;N. Merhav
Affiliations:
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa;-;-
Venue:
IEEE Transactions on Information Theory
Year:
1992

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Abstract

The generalized likelihood ratio test (GLRT), which is commonly used in composite hypothesis testing problems, is investigated. Conditions for asymptotic optimality of the GLRT in the Neyman-Pearson sense are studied and discussed. First, a general necessary and sufficient condition is established, and then based on this, a sufficient condition, which is easier to verify, is derived. A counterexample where the GLRT is not optimal, is provided as well. A conjecture is stated concerning the optimality of the GLRT for the class of finite-state sources