Composite Hypotheses and Generalized Likelihood Ratio Tests
نویسنده
چکیده
In many real world problems, it is difficult to precisely specify probability distributions. Our models for data may involve unknown parameters or other characteristics. Here are a few motivating examples. Example: Unknown amplitudes/delays in wireless communications. We don't always know how many relays a signal will go through, how strong the signal will be at each receiver, the distance between relay stations, etc. Example: Unknown signal amplitudes in functional brain imaging. Example: Unknown expression levels in gene microarray experiments.
منابع مشابه
A Law of Likelihood for Composite Hypotheses
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about extending the law to composite hypotheses, despite their tremendous relevance in statistical applications. This paper proposes a generalization of the law of lik...
متن کاملGeneralized Neyman–Pearson optimality of empirical likelihood for testing parameter hypotheses
This paper studies the Generalized Neyman–Pearson (GNP) optimality of empirical likelihood-based tests for parameter hypotheses. The GNP optimality focuses on the large deviation errors of tests, i.e., the convergence rates of the type I and II error probabilities under fixed alternatives. We derive (i) the GNP optimality of the empirical likelihood criterion (ELC) test against all alternatives...
متن کاملParametric Estimation and Tests through Divergences and Duality Technique
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple and composite hypotheses, extending maximum likelihood technique. An other view at the maximum likelihood approach, for estimation and test, is given. We prove...
متن کاملDegenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses
We propose the degenerate-generalized likelihood ratio test DGLRT for one-sided composite hypotheses in cases of independent and dependent observations. The theoretical results show that the DGLRT has controlled error probabilities and stops sampling with probability 1 under some regularity conditions. Moreover, its stopping boundaries are constants and can be easily determined using the provid...
متن کاملParametric estimation and tests through divergences and the duality technique
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple and composite hypotheses, extending maximum likelihood technique. An other view at the maximum likelihood approach, for estimation and test, is given. We prove...
متن کاملRobustness Evaluation in Sequential Testing of Composite Hypotheses
The problem of sequential testing of composite hypotheses is considered. Asymptotic expansions are constructed for the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of observations. To obtain these results a new approach based on approximation of the generalized likelihood ratio statistic by a specially constructed Markov chain i...
متن کامل