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A simple root \(n\) bandwidth selector. (English) Zbl 0745.62033
Summary: The asymptotically best bandwidth selectors for a kernel density estimator currently require the use of either unappealing higher order kernel pilot estimators or related Fourier transform methods. The point of this paper is to present a methodology which allows the fastest possible rate of convergence with the use of only nonnegative kernel estimators at all stages of the selection process. The essential idea is derived through careful study of factorizations of the pilot bandwidth in terms of the original bandwidth.

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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