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Article

A New Kernel Estimator of Copulas Based on Beta Quantile Transformations

Department of Econometrics, Riskcenter-IREA University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this paper.
Academic Editors: José María Sarabia and Manuel Alberto M. Ferreira
Mathematics 2021, 9(10), 1078; https://doi.org/10.3390/math9101078
Received: 26 March 2021 / Revised: 29 April 2021 / Accepted: 6 May 2021 / Published: 11 May 2021
A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis. View Full-Text
Keywords: nonparametric copula; kernel estimation; Beta transformation; extreme value copula nonparametric copula; kernel estimation; Beta transformation; extreme value copula
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MDPI and ACS Style

Bolancé, C.; Acuña, C.A. A New Kernel Estimator of Copulas Based on Beta Quantile Transformations. Mathematics 2021, 9, 1078. https://doi.org/10.3390/math9101078

AMA Style

Bolancé C, Acuña CA. A New Kernel Estimator of Copulas Based on Beta Quantile Transformations. Mathematics. 2021; 9(10):1078. https://doi.org/10.3390/math9101078

Chicago/Turabian Style

Bolancé, Catalina, and Carlos A. Acuña 2021. "A New Kernel Estimator of Copulas Based on Beta Quantile Transformations" Mathematics 9, no. 10: 1078. https://doi.org/10.3390/math9101078

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