Strong consistency and rates for recursive probability density estimators of stationary processes
type: Item
instance of: scholarly article
title: Strong consistency and rates for recursive probability density estimators of stationary processes
zbMATH Open document ID: 0619.62079
DOI: 10.1016/0047-259X(87)90077-7
author: Elias Masry
author: László Györfi
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: Authors's abstract: Let \(\{X_ j\}^{\infty}_{j=-\infty}\) be a vector-valued stationary process with a first-order univariate probability density f on \({\mathbb{R}}^ d\). Recursive estimation of f(x) from n not necessarily independent observations \(\{X_ j\}^ n_{j=1}\) is considered. For processes \(\{X_ j\}^{\infty}_{j=-\infty}\) which are asymptotically uncorrelated, sharp rates for the almost sure convergence of kernel-type estimators \(f_ n(x)\) are established.
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 4005391
zbMATH Keywords: density estimation
zbMATH Keywords: weakly dependent stationary processes
zbMATH Keywords: vector-valued stationary process
zbMATH Keywords: Recursive estimation
zbMATH Keywords: not necessarily independent observations
zbMATH Keywords: asymptotically uncorrelated
zbMATH Keywords: sharp rates for the almost sure convergence of kernel-type estimators
MaRDI profile type: Publication
cites work: Q4042488
cites work: Q5670093
cites work: Strong consistent density estimate from ergodic sample
cites work: Recursive probability density estimation for weakly dependent stationary processes
cites work: A maximal inequality and dependent strong laws
cites work: Q4084474
cites work: Q3914229
cites work: Remarks on some recursive estimators of a probability density
cites work: Q4135799
cites work: Asymptotically optimal discriminant functions for pattern classification
cites work: A Note on Permanents
full work available at URL: 0047-259x(87)90077-7
OpenAlex ID: W2064166825
description: scientific article; zbMATH DE number 4005391