THE UNIQUENESS OF CROSS-VALIDATION SELECTED SMOOTHING PARAMETERS IN KERNEL ESTIMATION OF NONPARAMETRIC MODELS
研究了多元非参数回归或条件概率函数的核估计中，交叉验证选择的平滑参数是否唯一的问题，给出了连续变量下的充要条件和混合变量下的充分条件。
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.