Hall, Peter On Kullback-Leibler loss and density estimation. (English) Zbl 0678.62045 Ann. Stat. 15, 1491-1519 (1987). The paper deals with optimal estimation of Kullback-Leibler loss and density function. The estimate of Kullback-Leibler loss is based on the non-parametric kernel density estimate. Its consistency and rate are studied and the smoothing parameter is chosen in the cross-validation approach. It is observed that the asymptotic properties of the estimate are profoundly influenced by the tails of both the kernel and the unknown density function. Standard consistency conditions on the smoothing sequence in density estimation such as \(h_ n\to 0\) and \(nh_ n\to \infty\) are not sufficient for expected Kullback-Leibler loss convergence. Reviewer: A.Krzyzak Cited in 59 Documents MSC: 62G05 Nonparametric estimation 62G99 Nonparametric inference 62H99 Multivariate analysis Keywords:discrimination information; tail properties; likelihood cross-validation; window width; optimal estimation of Kullback-Leibler loss; non-parametric kernel density estimate; smoothing parameter; asymptotic properties PDFBibTeX XMLCite \textit{P. Hall}, Ann. Stat. 15, 1491--1519 (1987; Zbl 0678.62045) Full Text: DOI