On the Hilbert kernel density estimate

Luc Devroye and Adam Krzyzak

Statistics & Probability Letters, 1999, vol. 44, issue 3, 299-308

Abstract: Let X be an -valued random variable with unknown density f. Let X1,...,Xn be i.i.d. random variables drawn from f. We study the pointwise convergence of a new class of density estimates, of which the most striking member is the Hilbert kernel estimatewhere Vd is the volume of the unit ball in . This is particularly interesting as this density estimate is basically of the format of the kernel estimate (except for the log n factor in front) and the kernel estimate does not have a smoothing parameter.

Keywords: Density; estimation; Kernel; estimate; Convergence; Bandwidth; selection; Nearest-neighbor; estimate; Nonparametric; estimation (search for similar items in EconPapers)
Date: 1999
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