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Near universal consistency of the maximum pseudolikelihood estimator for discrete models
Authors:Hien D Nguyen
Institution:Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia
Abstract:Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators subsume a large number of estimation techniques including ML estimators, maximum composite marginal likelihood estimators, and maximum pairwise likelihood estimators. When considering only the estimation of discrete models (on a possibly countably infinite support), we show that a simple finiteness assumption on an entropy-based measure is sufficient for assessing the consistency of the MPL estimator. As a consequence, we demonstrate that the MPL estimator of any discrete model on a bounded support will be consistent. Our result is valid in parametric, semiparametric, and nonparametric settings.
Keywords:primary  47N30  secondary  97K70  Consistency  Discrete models  Maximum pseudolikelihood estimation  Nonparametrics
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