When is the generalized likelihood ratio test optimal?

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 NeymanPearson 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 counterex...

Generalized Likelihood Ratio Test for Selecting

A generalized likelihood ratio test is considered for testing acoustic propagation models in the context of environmental parameter inversion. In the following, we use the term \hierarchy of models" to denote a sequence of model structures M1;M2;... in which each particular model structure Mn contains all previous ones as special cases. We propose a combined parameter estimation and multiple se...

Eliminating the Initial State for the Generalized Likelihood Ratio Test

Fault detection based on comparing a batch of data with a model of the system using the generalized likelihood ratio test is considered. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. There are two standard approaches to this problem. One is based on a parity space, where the influence of initial state is removed by projection, and t...

On sequential versions of the generalized likelihood ratio test

I t is shown that the Wilks large sample likelihood ratio statistic An, for testing between composite hypotheses 0O <= Q1 on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium OrnsteinUhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on An, which are the same whatever t...

Generalized Likelihood Ratio Statistics