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A Multivariate Local Likelihood Framework for Covariate-Dependent Copulas
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DOI：10.1007/s42519-026-00562-7.png)
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Abstract
En 中文
This paper develops a multivariate local likelihood framework for estimating covariate-dependent copulas of arbitrary dimension n >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 2$$\end{document} with multivariate covariates Y is an element of Rs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{Y} \in \mathbb {R}<^>s$$\end{document}. The proposed estimator generalizes existing bivariate approaches by locally maximizing the conditional copula log-likelihood with respect to a smooth calibration function linked to the copula parameter, thereby ensuring valid parameterization and capturing complex, heterogeneous dependence structures. Asymptotic theory is developed, including closed-form expressions for the bias, variance, and asymptotic normality of the estimator. Data-driven bandwidth and copula-family selection procedures based on cross-validation are proposed. Simulation studies demonstrate strong finite-sample performance of the estimator. An application to NHANES 2017-2018 glucose and glycohemoglobin data illustrates the method's interpretability and empirical value. Overall, this work provides the first comprehensive asymptotic and computational treatment of high-dimensional conditional copulas within the local likelihood framework.
Keywords:
Conditional copulas
Multivariate local likelihood estimation
Cross-validated bandwidth
Multivariate dependence
Kendall's tau
Journal
J
IF:
0.9
Papers:
85
Citations:
0
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