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Explicit solutions for the asymptotically optimal bandwidth in cross-validation

Author

Listed:
  • Karim M Abadir

    (Imperial College London)

  • Michel Lubrano

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, AMU - Aix Marseille Université)

Abstract

We show that least-squares cross-validation methods share a common structure that has an explicit asymptotic solution, when the chosen kernel is asymptotically separable in bandwidth and data. For density estimation with a multivariate Student-t(ν) kernel, the cross-validation criterion becomes asymptotically equivalent to a polynomial of only three terms. Our bandwidth formulae are simple and noniterative, thus leading to very fast computations, their integrated squared-error dominates traditional cross-validation implementations, they alleviate the notorious sample variability of cross-validation and overcome its breakdown in the case of repeated observations. We illustrate our method with univariate and bivariate applications, of density estimation and nonparametric regressions, to a large dataset of Michigan State University academic wages and experience.

Suggested Citation

  • Karim M Abadir & Michel Lubrano, 2024. "Explicit solutions for the asymptotically optimal bandwidth in cross-validation," Post-Print hal-04678541, HAL.
  • Handle: RePEc:hal:journl:hal-04678541
    DOI: 10.1093/biomet/asae007
    Note: View the original document on HAL open archive server: https://hal.science/hal-04678541
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    References listed on IDEAS

    as
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