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A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions

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  • Ichimura, Tsuyoshi
  • Fukuda, Daisuke

Abstract

Nonparametric conditional density functions are widely used in applied econometric and statistical modelling because they provide enriched information summaries of the relationships between dependent and independent variables. Although least-squares cross-validation is considered to be the best criterion for bandwidth selection of the kernel estimator of the conditional density, the number of computations required for this procedure grows exponentially as the number of observations increases. A fast algorithm is proposed to reduce this computational cost, and its accuracy and efficiency are verified via numerical experiments. A practical application is also presented to demonstrate the algorithm's potential usefulness.

Suggested Citation

  • Ichimura, Tsuyoshi & Fukuda, Daisuke, 2010. "A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3404-3410, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3404-3410
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    References listed on IDEAS

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    1. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    2. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    3. Racine, Jeff, 2002. "Parallel distributed kernel estimation," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 293-302, August.
    4. Bashtannyk, David M. & Hyndman, Rob J., 2001. "Bandwidth selection for kernel conditional density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 279-298, May.
    5. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    7. Jeffrey Racine, 2008. "Nonparametric econometrics: a primer (in Russian)," Quantile, Quantile, issue 4, pages 7-56, March.
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    Cited by:

    1. Fosgerau, Mogens & Fukuda, Daisuke, 2010. "Valuing travel time variability: Characteristics of the travel time distribution on an urban road," MPRA Paper 24330, University Library of Munich, Germany.

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