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.

翻译：本文研究了基于独立性copula某些扰动生成的马尔可夫链函数的参数估计量。我们给出了Longla(2023)中引入的多个copula族的copula参数极大似然估计量的渐近分布及置信区间。同时提出了另一类矩型估计量，并借助多元中心极限定理得到其渐近分布。我们重点研究了正弦copula、正弦-余弦copula以及扩展的Farlie-Gumbel-Morgenstern copula族生成的马尔可夫链特例，提出了若干独立性检验方法。针对这三个感兴趣的copula族进行了模拟研究，该模拟提出了两种新估计量与Longla和Peligrad(2021)稳健估计量的对比研究，展现了本文工作的优势。