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Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximumlikelihood (ML) estimators when likelihood functions are more difficult tomanipulate than their marginal and conditional components. Furthermore, MPLestimators subsume a large number of estimation techniques including MLestimators, maximum composite marginal likelihood estimators, and maximumpairwise likelihood estimators. When considering only the estimation ofdiscrete models (on a possibly countably infinite support), we show that asimple finiteness assumption on an entropy-based measure is sufficient forassessing the consistency of the MPL estimator. As a consequence, wedemonstrate that the MPL estimator of any discrete model on a bounded supportwill be consistent. Our result is valid in parametric, semiparametric, andnonparametric settings.

Near Universal Consistency of the Maximum Pseudolikelihood Estimator for Discrete Models