Explicit solutions for the asymptotically optimal bandwidth in cross-validation

• 成果类型: Article
• 署名作者: Abadir, Karim M.; Lubrano, Michel
• 署名单位: Imperial College London; Aix-Marseille Universite
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae007
• 发表日期: 2024
• 关键词: density; selection; robust; CHOICE

摘要

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(nu) 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.[Received on 15 March 2023. Editorial decision on 30 January 2024]