期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2007
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：We propose a new nonparametric estimator for the density function of multivariate bounded
data. As frequently observed in practice, the variable may be partially bounded (e.g.,
nonneative) 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 crossvalidation
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.
关键词：asymmetric kernels, multivariate boundary bias, nonparametric multivariate
density estimation, asymptotic properties, bandwidth selection, least squares crossvalidation.
