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Reducing variability of crossvalidation for smoothing-parameter choice

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  • Peter Hall
  • Andrew P. Robinson

Abstract

One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this compromises the performance of the estimators in which those parameters are used. We show that the variability can be reduced simply, significantly and reliably by employing bootstrap aggregation or bagging. We establish that in theory, when bagging is implemented using an adaptively chosen resample size, the variability of crossvalidation can be reduced by an order of magnitude. However, it is arguably more attractive to use a simpler approach, based for example on half-sample bagging, which can reduce variability by approximately 50%. Copyright 2009, Oxford University Press.

Suggested Citation

  • Peter Hall & Andrew P. Robinson, 2009. "Reducing variability of crossvalidation for smoothing-parameter choice," Biometrika, Biometrika Trust, vol. 96(1), pages 175-186.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:175-186
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    File URL: http://hdl.handle.net/10.1093/biomet/asn068
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    Cited by:

    1. Wang, Qing & Chen, Shiwen, 2015. "A general class of linearly extrapolated variance estimators," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 29-38.
    2. Wang, Qing & Lindsay, Bruce G., 2015. "Improving cross-validated bandwidth selection using subsampling-extrapolation techniques," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 51-71.
    3. Chu, Chi-Yang & Henderson, Daniel J. & Parmeter, Christopher F., 2017. "On discrete Epanechnikov kernel functions," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 79-105.
    4. Ricardo Cao, 2019. "Comments on: Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 664-670, September.

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