Pointwise consistency of the Hermite series density estimate
type: Item
instance of: scholarly article
title: Pointwise consistency of the Hermite series density estimate
zbMATH Open document ID: 0575.62042
DOI: 10.1016/0167-7152(85)90026-4
author: Włodzimierz Greblicki
author: M. Pawlak
published in: Statistics \& Probability Letters
publication date: 1985-01-01T00:00:00Z
review text: The Hermite series estimate of a density \(f\in L_ p\), \(p>1\), converges in the mean square to f(x) for almost all \(x\in {\mathbb{R}}\), if N(n)\(\to \infty\) and \(N(n)/n^ 2\to 0\) as \(n\to \infty\), where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is \(O(n^{-(2m-1)/2m})\). Results for complete convergence are also given.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 3919563
zbMATH Keywords: density estimation
zbMATH Keywords: mean square convergence
zbMATH Keywords: Hermite series estimate
zbMATH Keywords: mean square and weak consistency
Wikidata QID: Q118592640
MaRDI profile type: Publication
full work available at URL: 0167-7152(85)90026-4
OpenAlex ID: W2059196484
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description: scientific article; zbMATH DE number 3919563