# Near Universal Consistency of the Maximum Pseudolikelihood Estimator for Discrete Models

## TL;DR

This paper proves that the maximum pseudolikelihood estimator is consistently reliable for a wide range of discrete models, including parametric, semiparametric, and nonparametric cases, under a simple entropy condition.

## Contribution

It establishes the near-universal consistency of MPL estimators for discrete models with minimal assumptions, extending previous results to broader settings.

## Key findings

- MPL estimator is consistent for discrete models with bounded support.
- A simple entropy-based condition suffices for consistency.
- Results apply across parametric, semiparametric, and nonparametric frameworks.

## 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.