Recipient of the 2023 UConn Statistics Department Distinguished Alumnus Award
Nonparametric Estimation of Multivariate Copula using Empirical Bayes Method
Presented by Professor Sujit K. Ghosh, Ph.D., Department of Statistics, North Carolina State University
Wednesday, Sep 27 2023
4:00 PM-5:00 PM ET
Webex Meeting Link
In the field of finance, insurance, and 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 non-smooth and often not genuine copula, 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. In this paper, by using the so-called empirical checkerboard copula, we build a hierarchical empirical Bayes model that enables the estimation of a smooth copula function for arbitrary dimensions. The proposed estimator based on the multivariate Bernstein polynomials is itself a genuine copula, and the selection of its dimension-varying degrees is data-dependent. We also show that the proposed copula estimator provides a more accurate estimate of several multivariate dependence measures, which can be obtained in closed form. We investigate the asymptotic and finite-sample performance of the proposed estimator and compare it with some nonparametric estimators through simulation studies. An application to portfolio risk management is presented, along with a quantification of estimation uncertainty. [This presentation is based on a joint work with my former student Dr. Lu Lu]
Professor Sujit Kumar Ghosh has over 25 years of experience in conducting, applying, evaluating and documenting statistical analysis of biomedical and econometric and environmental data. Prof. Ghosh has supervised over 45 doctoral graduate students and received the Cavell Brownie Mentoring Award and D.D. Mason Faculty Award at NC State University. He has also served as a statistical investigator and consultant for over 45 different research projects funded by various leading private industries and federal agencies. Thus far, he has been invited to deliver over 185 lectures, seminars and courses at national and international meetings.
Prof. Ghosh has published over 135 refereed journal articles in the various areas of statistics with applications in biomedical and environmental sciences, econometrics and engineering. Prof. Ghosh received the International Indian Statistical Association (IISA) Young Investigator Award in 2008 and was elected a Fellow of the American Statistical Association (ASA) in 2009. He has served as the Program Director in the Division of Mathematical Sciences (DMS) at NSF in 2013-2014 and he has also served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute (SAMSI) in 2014-2017. Most recently, he served as the interim Department Head of Statistics at NC State in 2022-2023.