Nonparametric function estimation involving time series
type: Item
instance of: scholarly article
title: Nonparametric function estimation involving time series
zbMATH Open document ID: 0764.62038
author: Young K. Truong
author: Charles J. Stone
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: The authors study nonparametric estimation of the conditional expectation and the conditional median of \(Y\) given \(X=x\). The observations form a stationary strongly mixing sequence \((X_ t,Y_ t)\), \(t\in{\mathbf Z}\), with \(X_ t\in{\mathbf R}^ d\) and \(Y_ t\) real-valued. Examples include nonparametric prediction in a time series \((\xi_ t)\), where \(Y_ t=\xi_{t+m}\) and \(X_ t=(\xi_ t,\xi_{t-1},\dots,\xi_{t-d+1})\). The convergence rates of local averages, and local medians, respectively, are studied. For the right choice of bandwidth, these are shown to achieve the optimal convergence rates of \(n^{-1/(2+d)}\) pointwise and in \(L_ 2\), and \((n^{-1}\log n)^{1/(2+d)}\) in \(L_ \infty\).
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 61830
zbMATH Keywords: stationarity
zbMATH Keywords: conditional expectation
zbMATH Keywords: conditional median
zbMATH Keywords: stationary strongly mixing sequence
zbMATH Keywords: nonparametric prediction
zbMATH Keywords: time series
zbMATH Keywords: convergence rates of local averages
zbMATH Keywords: local medians
zbMATH Keywords: bandwidth
zbMATH Keywords: optimal convergence rates
reviewed by: Herold Dehling
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348513
OpenAlex ID: W2053672153
DOI: 10.1214/AOS/1176348513
description: scientific article; zbMATH DE number 61830