Explicit solutions for the asymptotically optimal bandwidth in cross-validation

Karim Abadir () and Michel Lubrano
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Karim Abadir: Imperial College London

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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.

Keywords: Academic wage distribution; Bandwidth choice; Cross-validation; Explicit analytical solution; Nonparametric density estimation (search for similar items in EconPapers)
Date: 2024-02-12
Note: View the original document on HAL open archive server: https://hal.science/hal-04678541
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Published in Biometrika, 2024, ⟨10.1093/biomet/asae007⟩

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Related works:
Journal Article: Explicit solutions for the asymptotically optimal bandwidth in cross-validation (2024)
Working Paper: Explicit solutions for the asymptotically-optimal bandwidth in cross validation (2023)
Working Paper: Explicit solutions for the asymptotically-optimal bandwidth in cross validation (2023)
Working Paper: EXPLICIT SOLUTIONS FOR THE ASYMPTOTICALLY-OPTIMAL BANDWIDTH IN CROSS VALIDATION (2010)
Working Paper: Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04678541

DOI: 10.1093/biomet/asae007

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