Semiparametric multivariate density estimation for positive data using copulas

Authors:
T. Bouezmarni;J. V. K. Rombouts
Affiliations:
HEC Montréal, Canada and Institute of Statistics, Université catholique de Louvain, Canada;HEC Montréal, Canada and CIRANO, Canada and CIRPEE, Canada and CORE, Université catholique de Louvain, Canada
Venue:
Computational Statistics & Data Analysis
Year:
2009

Citing 3
Cited 1

Smooth estimators of distribution and density functions

Computational Statistics & Data Analysis - Second special issue on optimization techniques in statistics
Asymptotic efficiency of the two-stage estimation method for copula-based models

Journal of Multivariate Analysis
Comparison of semiparametric and parametric methods for estimating copulas

Computational Statistics & Data Analysis

Asymptotic properties of the Bernstein density copula estimator for α-mixing data

Journal of Multivariate Analysis

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Abstract

The 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.