When Composite Likelihood meets Stochastic Approximation

doi:10.1080/01621459.2024.2436219

Return

When Composite Likelihood meets Stochastic Approximation

2025-01-31

PRE

Giuseppe Alfonzetti *

Ruggero Bellio

Yunxiao Chen

Irini Moustaki

DOI：10.1080/01621459.2024.2436219

Original

Original request for help

Save

Abstract

En 中文

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inferences when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This article tackles this challenge by employing an approximation of the conventional composite likelihood estimator based on a stochastic optimization procedure. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Keywords:

Exchangeable variables central limit theorem

Gamma frailty model

Ising model

Pairwise likelihood

Stochastic gradient