Asymptotic distribution of smoothers based on local means and local medians under dependence
type: Item
instance of: scholarly article
title: Asymptotic distribution of smoothers based on local means and local medians under dependence
zbMATH Open document ID: 0898.62043
author: Graciela Boente
author: Ricardo Fraiman
published in: Journal of Multivariate Analysis
publication date: 1998-11-05T00:00:00Z
review text: Let \(\{(X_t,Y_t)\), \(t\geq p+1\}\) be a strictly stationary process, \(X_t\in \mathbb{R}^p\), \(Y_t\in \mathbb{R}\), with the same distribution function as the vector \((X,Y)\). We will study the asymptotic distribution of some nonparametric estimators of the conditional expectation \(r(x)= E(Y\mid X=x)\). As is well known, if we allow dependence on the observed sample, this framework includes usual nonparametric regression with dependent errors. Also, autoregressive models can be considered by taking \(X_t= (Y_{t-1},\dots, Y_{t-p})\).
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 797142
zbMATH Keywords: k th nearest neighbor regression
zbMATH Keywords: uniform nearest neighbor weights
zbMATH Keywords: local means
zbMATH Keywords: local medians
zbMATH Keywords: strictly stationary process
zbMATH Keywords: conditional expectation
zbMATH Keywords: nonparametric regression
zbMATH Keywords: dependent errors
zbMATH Keywords: autoregressive models
MaRDI profile type: Publication
full work available at URL: jmva.1995.1045
OpenAlex ID: W2093682741
DOI: 10.1006/JMVA.1995.1045
description: scientific article; zbMATH DE number 797142