A simple root n bandwidth selector

Jones, M. C.; Marron, J. S. and Park, B. U. (1991). A simple root n bandwidth selector. Annals of Statistics, 19(4) pp. 1919–1932.

DOI: https://doi.org/10.1214/aos/1176348378

Abstract

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.

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