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Bagging cross-validated bandwidth selection in nonparametric regression estimation with applications to large-sized samples

Author

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  • Barreiro-Ures, Daniel
  • Cao, Ricardo
  • Francisco-Fernández, Mario
  • Fernández-Casal, Rubén

Abstract

Cross-validation is a well-known and widely used bandwidth selection method in nonparametric regression estimation. However, this technique has two remarkable drawbacks: (i) the large variability of the selected bandwidths, and (ii) the inability to provide results in a reasonable time for very large sample sizes. To address these issues, bagged cross-validation bandwidth selectors are investigated. This approach consists in computing the cross-validation bandwidths for a finite number of subsamples and then rescaling the averaged smoothing parameters to the original sample size. Under a random-design regression model, asymptotic expressions up to a second-order for the bias and variance of the leave-one-out cross-validation bandwidth for the Nadaraya–Watson estimator are obtained. Subsequently, the asymptotic bias and variance and the limiting distribution for the bagged cross-validation selector are derived. Suitable choices of the number of subsamples and the subsample size lead to a convergence rate proportional to the inverse square root of the sample size for the bagging cross-validation selector, outperforming the slower rate typically associated with leave-one-out cross-validation. Several simulations and an illustration on a real dataset related to the COVID-19 pandemic show the behavior of our proposal and its better performance, in terms of statistical efficiency and computing time, when compared to leave-one-out cross-validation.

Suggested Citation

  • Barreiro-Ures, Daniel & Cao, Ricardo & Francisco-Fernández, Mario & Fernández-Casal, Rubén, 2026. "Bagging cross-validated bandwidth selection in nonparametric regression estimation with applications to large-sized samples," Computational Statistics & Data Analysis, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:csdana:v:213:y:2026:i:c:s0167947325001331
    DOI: 10.1016/j.csda.2025.108257
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    References listed on IDEAS

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    1. D Barreiro-Ures & R Cao & M Francisco-Fernández & J D Hart, 2021. "Bagging cross-validated bandwidths with application to big data [baggedcv: Bagged cross-validation for kernel density bandwidth selection]," Biometrika, Biometrika Trust, vol. 108(4), pages 981-988.
    2. Max Köhler & Anja Schindler & Stefan Sperlich, 2014. "A Review and Comparison of Bandwidth Selection Methods for Kernel Regression," International Statistical Review, International Statistical Institute, vol. 82(2), pages 243-274, August.
    3. 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.
    4. Peter Hall & Andrew P. Robinson, 2009. "Reducing variability of crossvalidation for smoothing-parameter choice," Biometrika, Biometrika Trust, vol. 96(1), pages 175-186.
    5. Inés Barbeito & Ricardo Cao & Stefan Sperlich, 2023. "Bandwidth selection for statistical matching and prediction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 418-446, March.
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