Estimation problems for some perturbations of the independence copula

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.