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

Published online by Cambridge University Press:  22 August 2005

Qi Li  and
Jianxin Zhou
Qi Li
Affiliation:
Texas A&M University and Tsinghua University
Jianxin Zhou
Affiliation:
Texas A&M University
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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.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 21 , Issue 5 , October 2005 , pp. 1017 - 1025
Copyright
© 2005 Cambridge University Press

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