Semiparametric Multivariate Density Estimation for Positive Data Using Copulas

CORE Discussion Paper No. 2007/54

28 Pages Posted: 30 Aug 2007

See all articles by Taoufik Bouezmarni

Taoufik Bouezmarni

HEC Montreal

J. V. K. Rombouts

HEC Montreal; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE); Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: July 26, 2007

Abstract

In this paper we estimate density functions for positive multivariate data. We propose a semiparametric approach. The estimator combines gamma kernels or local linear kernels, also called boundary kernels, for the estimation of the marginal densities with semiparametric copulas to model the dependence. This semiparametric approach is robust both to the well known boundary bias problem and the curse of dimensionality problem. We derive the mean integrated squared error properties, including the rate of convergence, the uniform strong consistency and the asymptotic normality. A simulation study investigates the finite sample performance of the estimator. We find that univariate least squares cross validation, to choose the bandwidth for the estimation of the marginal densities, works well and that the estimator we propose performs very well also for data with unbounded support. Applications in the field of finance are provided.

Keywords: Asymptotic properties, asymmetric kernels, boundary bias, copula, curse of dimension, least squares cross validation

Suggested Citation

Bouezmarni, Taoufik and Rombouts, Jeroen, Semiparametric Multivariate Density Estimation for Positive Data Using Copulas (July 26, 2007). CORE Discussion Paper No. 2007/54, Available at SSRN: https://ssrn.com/abstract=1010659 or http://dx.doi.org/10.2139/ssrn.1010659

Taoufik Bouezmarni (Contact Author)

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Jeroen Rombouts

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE) ( email )

Pavillon De Sève
Ste-Foy, Quebec G1K 7P4
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
119
Abstract Views
619
rank
261,143
PlumX Metrics