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A local cross-validation algorithm

Author

Listed:
  • Hall, Peter
  • Schucany, William R.

Abstract

The usuall form of cross-validation is global in character, and is designed to estimate a density in some "average" sense over its entire support. In this paper we present a local version of squared-error cross-validation, suitable for estimating a probability density at a given point. It is shown theoretically to be asymptotically optimal in the sense of minimizing mean squared error. Numerical examples illustrate finite sample characteristic, and show that local cross-validation is a practical algorithm.

Suggested Citation

  • Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:2:p:109-117
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    Citations

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    Cited by:

    1. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    2. A. Quintela del Río & J. Vilar Fernández, 1992. "A local cross-validation algorithm for dependent data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 123-153, December.
    3. Tingting Cheng & Jiti Gao & Xibin Zhang, 2019. "Nonparametric localized bandwidth selection for Kernel density estimation," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 733-762, August.
    4. Cristina Butucea, 2001. "Numerical results concerning a sharp adaptive density estimator," Computational Statistics, Springer, vol. 16(2), pages 271-298, July.
    5. Luc Devroye & Gábor Lugosi, 1998. "Variable Kernel estimates: On the impossibility of tuning the parameters," Economics Working Papers 325, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    7. Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, University Library of Munich, Germany.
    8. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    9. Sam Astill & David I Harvey & Stephen J Leybourne & A M Robert Taylor & Yang Zu, 2023. "CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 21(1), pages 187-227.

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