Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods

Lu Lu () and Sujit Ghosh
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Lu Lu: Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA
Sujit Ghosh: Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA

Mathematics, 2023, vol. 11, issue 20, 1-22

Abstract: In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are nonsmooth and often not genuine copulas, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. Additionally, the proposed copula estimator is shown to provide a more accurate estimate of several multivariate dependence measures. Both theoretical asymptotic properties and finite-sample performances of the proposed estimator based on simulated data are presented and compared with some nonparametric estimators. An application to portfolio risk management is included based on stock prices data.

Keywords: Bernstein copula; dependence measures; empirical checkerboard copula; financial data; uncertainty quantification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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