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Title: Nonparametric Density Estimation for Multivariate Bounded Data
Authors: Bouezmarni, Taoufik
Rombouts, Jeroen V.K.
Keywords: Asymmetric kernels
Multivariate boundary bias
Nonparametric multivariate density estimation
Asymptotic properties
Bandwidth selection
Least squares cross-validation
Issue Date: 2007-10
Series/Report no.: Cahiers du CIRPÉE;07-32
Abstract: We propose a new nonparametric estimator for the density function of multivariate bounded data. As frequently observed in practice, the variables may be partially bounded (e.g., nonnegative) or completely bounded (e.g., in the unit interval). In addition, the variables may have a point mass. We reduce the conditions on the underlying density to a minimum by proposing a nonparametric approach. By using a gamma, a beta, or a local linear kernel (also called boundary kernels), in a product kernel, the suggested estimator becomes simple in implementation and robust to the well known boundary bias problem. We investigate the mean integrated squared error properties, including the rate of convergence, uniform strong consistency and asymptotic normality. We establish consistency of the least squares cross-validation method to select optimal bandwidth parameters. A detailed simulation study investigates the performance of the estimators. Applications using lottery and corporate finance data are provided.
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