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The Uniqueness Of Cross-Validation Selected Smoothing Parameters In Kernel Estimation Of Nonparametric Models

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  • Li, Qi
  • Zhou, Jianxin

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.

Suggested Citation

  • Li, Qi & Zhou, Jianxin, 2005. "The Uniqueness Of Cross-Validation Selected Smoothing Parameters In Kernel Estimation Of Nonparametric Models," Econometric Theory, Cambridge University Press, vol. 21(5), pages 1017-1025, October.
    • Handle: RePEc:cup:etheor:v:21:y:2005:i:05:p:1017-1025_05
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    Cited by:

    1. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    2. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. Li, Zheng & Rejesus, Roderick M. & Zheng, Xiaoyong, 2018. "Nonparametric Estimation and Inference of Production Risk with Categorical Variables," 2018 Annual Meeting, August 5-7, Washington, D.C. 274400, Agricultural and Applied Economics Association.
    5. Offermanns, Christian J., 2014. "On the degree of homogeneity in dynamic heterogeneous panel data models," Discussion Papers 2014/25, Free University Berlin, School of Business & Economics.
    6. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.

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