Variable window width kernel estimates of probability densities. (English) Zbl 0637.62036

Hall, Peter; Marron, J. S.

Probab. Theory Relat. Fields 80, No. 1, 37-49 (1988).

Kernel density estimators which allow different amounts of smoothing at different locations are studied. Modifications of estimators proposed by L. Breiman, W. Meisel and E. Purcell [Technometrics 19, 135-144 (1977; Zbl 0379.62023)] and I. S. Abramson [Ann. Stat. 10, 1217-1223 (1982; Zbl 0507.62040)], which have variable window widths, are seen to have very fast rates of convergence. These rates have traditionally been obtained using a less natural higher order kernel, which has the disadvantage of allowing an estimator which takes on negative values.

Reviewer: P.Hall

MSC:

62G05	Nonparametric estimation
62E20	Asymptotic distribution theory in statistics

Keywords:

kernel density estimators; smoothing at different locations; variable window widths; fast rates of convergence

References:

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