On the use of compactly supported density estimates in problems of discrimination
Journal of Multivariate Analysis
On the performance of kernel estimators for high-dimensional, sparse binary data
Journal of Multivariate Analysis
Kernel estimators for cell probabilities
Journal of Multivariate Analysis
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Computer Vision and Image Understanding
Nonparametric estimation of the anisotropic probability density of mixed variables
Journal of Multivariate Analysis
Hi-index | 0.00 |
In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their 'benchmark' optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.