Robustness properties of marginal composite likelihood estimators

TL;DR

This paper investigates the robustness of marginal composite likelihood estimators, demonstrating through an example that they can be inconsistent under model misspecification, unlike maximum likelihood estimators.

Contribution

It provides a critical analysis showing that composite likelihood estimators may lack robustness, challenging assumptions about their advantages over full likelihood methods.

Findings

Composite likelihood estimators can be inconsistent under misspecification

Maximum likelihood estimators remain consistent despite model misspecification

Robustness of composite likelihoods is not guaranteed in practice

Abstract

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full distribution of the response, which means that in some situations the resulting estimator will be more robust to model misspecification than the maximum likelihood estimator. The purpose of this note is to show that such increased robustness is not guaranteed. An example is given in which various marginal composite likelihood estimators are inconsistent under model misspecification, even though the maximum likelihood estimator is consistent.