Near universal consistency of the maximum pseudolikelihood estimator for discrete models |
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Authors: | Hien D Nguyen |
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Institution: | Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia |
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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. |
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Keywords: | primary 47N30 secondary 97K70 Consistency Discrete models Maximum pseudolikelihood estimation Nonparametrics |
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