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A local cross-validation algorithm


  • Hall, Peter
  • Schucany, William R.


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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    Cited by:

    1. Tingting Cheng & Jiti Gao & Xibin Zhang, 2016. "Nonparametric Localized Bandwidth Selection for Kernel Density Estimation," Monash Econometrics and Business Statistics Working Papers 7/16, Monash University, Department of Econometrics and Business Statistics.
    2. 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.
    3. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    4. 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.
    5. Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, EconWPA.


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