Estimation problems for some perturbations of the independence copula

TL;DR

This paper studies parameter estimation methods for perturbations of the independence copula using Markov chains, deriving asymptotic distributions, proposing new estimators, and comparing their performance through simulations.

Contribution

It introduces new moment-like estimators and asymptotic results for perturbations of the independence copula, including sine, sine-cosine, and Farlie-Gumbel-Morgenstern families.

Findings

Asymptotic distributions of maximum likelihood estimators derived.

Proposed estimators show advantages over existing robust methods.

Simulation results compare estimator performances across copula families.

Abstract

This work provides a study of parameter estimators based on functions of Markov chains generated by some perturbations of the independence copula. We provide asymptotic distributions of maximum likelihood estimators and confidence intervals for copula parameters of several families of copulas introduced in Longla (2023). Another set of moment-like estimators is proposed along with a multivariate central limit theorem, that provides their asymptotic distributions. We investigate the particular case of Markov chains generated by sine copulas, sine-cosine copulas and the extended Farlie-Gumbel-Morgenstern copula family. Some tests of independence are proposed. A simulation study is provided for the three copula families of interest. This simulation proposes a comparative study of the two introduced estimators and the robust estimator of Longla and Peligrad (2021), showing advantages of the proposed work.