THE UNIQUENESS OF CROSS-VALIDATION SELECTED SMOOTHING PARAMETERS IN KERNEL ESTIMATION OF NONPARAMETRIC MODELS

Qi Li and Jianxin Zhou

Econometric Theory, 2005, vol. 21, issue 5, 1017-1025

Abstract: We investigate the issue of the uniqueness of the cross-validation selected smoothing parameters in kernel estimation of multivariate nonparametric regression or conditional probability functions. When the covariates are all continuous variables, we provide a necessary and sufficient condition, and when the covariates are a mixture of categorical and continuous variables, we provide a simple sufficient condition that guarantees asymptotically the uniqueness of the cross-validation selected smoothing parameters.We thank a referee for the constructive comments.

Date: 2005
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