SMOOTHED CROSS-VALIDATION

• 成果类型: Article
• 署名作者: HALL, P; MARRON, JS; PARK, BU
• 署名单位: Seoul National University (SNU)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01205233
• 发表日期: 1992
• 页码: 1-20
• 关键词: squared density derivatives; bootstrap choice; estimators; bandwidth; selection; point; error

摘要

For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be best possible under a wide range of smoothness conditions. The method is more appealing than other selectors with this property, because its motivation is not heavily dependent on precise asymptotic analysis, and because its form is simple and intuitive. Theory is also given for choice of the amount of presmoothing, and this is used to derive a data-based method for this choice.