Parametric and semiparametric approaches for copula-based regression estimation

Year 2024, , 1141 - 1157, 27.08.2024

Alam Ali , Ashok Pathak , Mohd Arshad

https://doi.org/10.15672/hujms.1359072

Abstract

Based on the normality assumption on dependent variable, regression analysis is one of the most popular statistical techniques for studying the dependence between response and explanatory variables. However, violation of this assumption in the data makes regression analysis inappropriate in several real life situations. Copula is a powerful tool for modeling multivariate data and have recently been employed in regression analysis. The key concept behind copula-based regression approach is to formulate conditional expectation in terms of copula density and marginal distributions. In this paper, we explore parametric and semiparametric estimations of the copula-based regression function. The maximum likelihood (ML), inference functions for margins (IFM), and pseudo maximum likelihood (PML) techniques are adopted here for estimation purposes. Extensive numerical experiments are performed to illustrate the performance of the proposed copula-based regression estimators under specified and misspecified scenarios of copulas and marginals. Finally, two real data applications are also presented to demonstrate the performance of the considered estimators.

Keywords

Copula-based regression estimation, dependence modelling, regression function, inference function for margins (IFM), semiparametric inference

Ethical Statement

No potential conflict of interest was reported by thrauthor(s)

Supporting Institution

Department of Science and Technology (DST), Government of India

Project Number

IF 190682

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