Consistent nonparametric multiple regression: the fixed design case
type: Item
instance of: scholarly article
title: Consistent nonparametric multiple regression: the fixed design case
zbMATH Open document ID: 0637.62044
DOI: 10.1016/0047-259X(88)90155-8
author: Alexander A. Georgiev
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: Consider the nonparametric regression model \(Y_ i^{(n)}=g(x_ i^{(n)})+\epsilon_ i^{(n)}\), \(i=1,...,n\), where \(g\) is an unknown function, the design points \(x_ i^{(n)}\) are known and nonrandom, and \(\epsilon_ i^{(n)}\)'s are independent random variables. The regressor is assumed to take values in \(A\subset \mathbb R^ p\), and the regressand to be real valued. This paper studies the behavior of the general nonparametric estimate \[ g_ n(x)=\sum^{n}_{i=1}w_{ni}(x)Y_ i^{(n)}, \] where the weight function \(w_{ni}\) is of the form \(w_{ni}(x)=w_{ni}(x;x_ i^{(n)},\dots,x_ n^{(n)})\). Under suitable conditions, it is shown that the general linear smoother \(g_ n\) for the unknown rendent variable.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 4039029
zbMATH Keywords: kernel estimate
zbMATH Keywords: nearest neighbor estimate
zbMATH Keywords: orthogonal series estimate
zbMATH Keywords: splines
zbMATH Keywords: law of large numbers
zbMATH Keywords: central limit theorem
zbMATH Keywords: consistency
zbMATH Keywords: general linear smoother
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4039029