Estimation problems for some perturbations of the independence copula
Location
Room 321, Hume Hall
Start Date
27-4-2024 10:00 AM
End Date
27-4-2024 11:00 AM
Description
In this work, we consider symmetric copulas with density of the form: ∞ C(u,v) = 1+ i=1 λkφk(u)φk(v) (1) where {φk(x),k ∈ N} is an orthogonal basis of L2(0,1) and the sequence |λk| has a finite number of values or converges to 0. For the finite case, we propose an estimator of the vector λ = (λ1,...,λs) by considering the Markov chains generated by the copula using uniform margins as stationary distribution. In order to determine the confidence interval of parameters, we provide a multivariate central limit theorem for the vector λ. a For s = 2, several examples are considered such as the cosine copula, the sinecosine copula and the Legendre copula. For each of those copulas, we determine the estimators of the parameters and the central limit theorem as well. A simulation study is provided with a comparison to other known estimators such as MLE and that of Longla and Peligrad (2021). [A formatted abstract is also attached.]
Relational Format
conference proceeding
Recommended Citation
Longla, Martial and Hamadou, Mous-Abou, "Estimation problems for some perturbations of the independence copula" (2024). AMS-AWM Student Research Symposium. 10.
https://egrove.olemiss.edu/ams_awm_sympo/2024/schedule/10
Estimation problems for some perturbations of the independence copula
Room 321, Hume Hall
In this work, we consider symmetric copulas with density of the form: ∞ C(u,v) = 1+ i=1 λkφk(u)φk(v) (1) where {φk(x),k ∈ N} is an orthogonal basis of L2(0,1) and the sequence |λk| has a finite number of values or converges to 0. For the finite case, we propose an estimator of the vector λ = (λ1,...,λs) by considering the Markov chains generated by the copula using uniform margins as stationary distribution. In order to determine the confidence interval of parameters, we provide a multivariate central limit theorem for the vector λ. a For s = 2, several examples are considered such as the cosine copula, the sinecosine copula and the Legendre copula. For each of those copulas, we determine the estimators of the parameters and the central limit theorem as well. A simulation study is provided with a comparison to other known estimators such as MLE and that of Longla and Peligrad (2021). [A formatted abstract is also attached.]
Comments
poster