Hall, Peter Large sample optimality of least squares cross-validation in density estimation. (English) Zbl 0599.62051 Ann. Stat. 11, 1156-1174 (1983). Cross-validatory methods in density estimation have generated considerable interest in recent years. Early methods, however, where shown to produce inconsistent estimators unless the distribution tails are very small. A modification was suggested by Bowman and Rudemo using a least squares cross-validation method. In this paper the author proves that the Bowman-Rudemo method minimizes the integrated square error in an asymptotic sense with tail conditions which are only slightly more severe than the hypothesis of finite variance. Cited in 1 ReviewCited in 53 Documents MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62H12 Estimation in multivariate analysis Keywords:large sample optimality; density estimation; least squares cross- validation method; integrated square error PDFBibTeX XMLCite \textit{P. Hall}, Ann. Stat. 11, 1156--1174 (1983; Zbl 0599.62051) Full Text: DOI