Semiparametric multivariate density estimation for positive data using copulas
AbstractThe estimation of density functions for positive multivariate data is discussed. The proposed approach is semiparametric. The estimator combines gamma kernels or local linear kernels, also called boundary kernels, for the estimation of the marginal densities with parametric copulas to model the dependence. This semiparametric approach is robust both to the well-known boundary bias problem and the curse of dimensionality problem. Mean integrated squared error properties, including the rate of convergence, the uniform strong consistency and the asymptotic normality are derived. A simulation study investigates the finite sample performance of the estimator. The proposed estimator performs very well, also for data without boundary bias problems. For bandwidths choice in practice, the univariate least squares cross validation method for the bandwidth of the marginal density estimators is investigated. Applications in the field of finance are provided.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 53 (2009)
Issue (Month): 6 (April)
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Web page: http://www.elsevier.com/locate/csda
Other versions of this item:
- BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Semiparametric multivariate density estimation for positive data using copulas," CORE Discussion Papers 2007054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Semiparametric Multivariate Density Estimation for Positive Data Using Copulas," Cahiers de recherche 07-08, HEC Montréal, Institut d'économie appliquée.
- Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2007. "Semiparametric Multivariate Density Estimation for Positive Data Using Copulas," Cahiers de recherche 0731, CIRPEE.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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