Explicit solutions for the asymptotically optimal bandwidth in cross-validation

Karim M Abadir and Michel Lubrano

Biometrika, 2024, vol. 111, issue 3, 809-823

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
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Related works:
Working Paper: 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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