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