Bandwidth selection for kernel density estimation. (English) Zbl 0749.62022

Chiu, Shean-Tsong

Ann. Stat. 19, No. 4, 1883-1905 (1991).

From the author’s abstract: The problem of automatic bandwidth selection for a kernel density estimator is considered. Based on characteristic functions, an important expression for the cross-validation bandwidth estimate is obtained. On its basis it is shown that a certain stabilized bandwidth selector gives a strongly consistent estimate of the optimal bandwidth. For sufficiently smooth density functions it is shown that the stabilized bandwidth estimate is asymptotically normal with a relative convergence rate \(n^{-1/2}\) instead of \(n^{-1/10}\) for the cross- validation estimate. A plug-in estimate and an adjusted plug-in estimate are proposed and their asymptotic distributions are obtained. Simulation results verify that the proposed procedures perform much better than the cross-validation for finite samples.

Reviewer: P.Gänßler (München)

MSC:

62G07	Density estimation
62G20	Asymptotic properties of nonparametric inference
62E20	Asymptotic distribution theory in statistics

Keywords:

automatic bandwidth selection; kernel density estimator; characteristic functions; cross-validation bandwidth estimate; strongly consistent estimates; optimal bandwidth; smooth density functions; asymptotic normality; convergence rate; plug-in estimate; adjusted plug-in estimate; simulation results