Reducing variability of crossvalidation for smoothing-parameter choice

• 成果类型: Article
• 署名作者: Hall, Peter; Robinson, Andrew P.
• 署名单位: University of Melbourne
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn068
• 发表日期: 2009
• 页码: 175186
• 关键词: generalized cross-validation; integrated square error; bandwidth selection; bootstrap choice; density

摘要

One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this compromises the performance of the estimators in which those parameters are used. We show that the variability can be reduced simply, significantly and reliably by employing bootstrap aggregation or bagging. We establish that in theory, when bagging is implemented using an adaptively chosen resample size, the variability of crossvalidation can be reduced by an order of magnitude. However, it is arguably more attractive to use a simpler approach, based for example on half-sample bagging, which can reduce variability by approximately 50%.