High-dimensional factor copula models with estimation of latent variables

TL;DR

This paper introduces high-dimensional factor copula models that efficiently estimate latent variables and their dependence structures, leveraging proxies and sequential procedures to improve computational feasibility and estimation accuracy.

Contribution

It proposes a novel framework for high-dimensional factor copula models utilizing proxies for latent variables, enabling scalable estimation without predefined copula families.

Findings

Proxies are consistent for latent variables as sample size and observed variables increase.

Sequential procedures facilitate latent variable estimation, copula selection, and parameter estimation.

Approximate log-likelihoods reduce computational effort in copula parameter estimation.

Abstract

Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor scores or proxies are defined as conditional expectations of latent variables given the observed variables. With mild assumptions, the proxies are consistent for corresponding latent variables as the sample size and the number of observed variables linked to each latent variable go to infinity. When the bivariate copulas linking observed variables to latent variables are not assumed in advance, sequential procedures are used for latent variables estimation, copula family selection and parameter estimation. The use of proxy variables for factor copulas means that approximate log-likelihoods can be used to estimate copula parameters with less computational effort for numerical integration.