When is the generalized likelihood ratio test optimal?

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. >

[1]  W. Hoeffding Asymptotically Optimal Tests for Multinomial Distributions , 1965 .

[2]  Neri Merhav,et al.  On the estimation of the order of a Markov chain and universal data compression , 1989, IEEE Trans. Inf. Theory.

[3]  Michael Gutman,et al.  Asymptotically optimal classification for multiple tests with empirically observed statistics , 1989, IEEE Trans. Inf. Theory.

[4]  Neri Merhav,et al.  Estimating the number of states of a finite-state source , 1992, IEEE Trans. Inf. Theory.

[5]  E. S. Pearson,et al.  ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I , 1928 .

[6]  Richard E. Blahut,et al.  Principles and practice of information theory , 1987 .

[7]  Jacob Ziv,et al.  On classification with empirically observed statistics and universal data compression , 1988, IEEE Trans. Inf. Theory.

[8]  Neri Merhav,et al.  The estimation of the model order in exponential families , 1989, IEEE Trans. Inf. Theory.

[9]  Abraham Lempel,et al.  Compression of individual sequences via variable-rate coding , 1978, IEEE Trans. Inf. Theory.

[10]  Giuseppe Longo,et al.  The error exponent for the noiseless encoding of finite ergodic Markov sources , 1981, IEEE Trans. Inf. Theory.

[11]  I. Csiszár $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[12]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[13]  Ofer Zeitouni,et al.  On universal hypotheses testing via large deviations , 1991, IEEE Trans. Inf. Theory.

[14]  Neri Merhav,et al.  A Bayesian classification approach with application to speech recognition , 1991, IEEE Trans. Signal Process..

[15]  A. Gualtierotti H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .