Semiparametric Multivariate Density Estimation for Positive Data Using Copulas

Taoufik Bouezmarni and Jeroen Rombouts

No 07-08, Cahiers de recherche from HEC Montréal, Institut d'économie appliquée

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. (search for similar items in EconPapers)
Pages: 32 pages
Date: 2007-07
New Economics Papers: this item is included in nep-ecm and nep-fmk
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http://www.hec.ca/iea/cahiers/2007/iea0708_jrombouts.pdf (application/pdf)

Related works:
Journal Article: Semiparametric multivariate density estimation for positive data using copulas (2009)
Working Paper: Semiparametric multivariate density estimation for positive data using copulas (2007)
Working Paper: Semiparametric Multivariate Density Estimation for Positive Data Using Copulas (2007)
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