THE UNIQUENESS OF CROSS-VALIDATION SELECTED SMOOTHING PARAMETERS IN KERNEL ESTIMATION OF NONPARAMETRIC MODELS
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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. © 2005 Cambridge University Press.
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