Universal inference with composite likelihoods

TL;DR

This paper introduces a universal inference method using composite likelihoods, enabling valid confidence sets and hypothesis tests for complex models without requiring full joint distribution specification.

Contribution

It presents a novel approach to construct finite-sample valid inference procedures from any estimator using composite likelihood ratios.

Findings

Valid confidence sets and tests are achievable with composite likelihoods.

Method demonstrated through simulation with bivariate models.

Universal applicability to various estimators and models.

Abstract

Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable joint specification. We demonstrate that generic composite likelihoods consisting of marginal and conditional specifications permit the simple construction of composite likelihood ratio-like statistics from which finite-sample valid confidence sets and hypothesis tests can be constructed. These statistics are universal in the sense that they can be constructed from any estimator for the parameter of the underlying DGP. We demonstrate our methodology via a simulation study using a pair of conditionally specified bivariate models.