Robust regression designs when the design space consists of finitely many points
type: Item
instance of: scholarly article
title: Robust regression designs when the design space consists of finitely many points
zbMATH Open document ID: 0546.62048
author: Ker-Chau Li
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: The author considers the model \(Y_ i=\alpha +\beta x_ i+g(x_ i)+\epsilon_ i\), \(i=1,2,...,n\), where \(\{\epsilon_ i\}\) are uncorrelated random variables with mean 0 and variance \(\sigma^ 2\), \(x_ i\in X=\{k/2N,-k/2N|\quad k=1,2,...,N\}\) for some fixed positive integer \(N\geq 3\) and \[ g\in G=\{h|\quad | h(x)|\leq \delta,\quad\min_{\alpha,\beta}\int (h(x)-\alpha -\beta x)^ 2d\mu (x)=\int h^ 2(x)d\mu (x)\}, \] with \(\delta \geq 0\) and \(\mu\) the uniform probability measure on X. The loss function \(\omega_ 1(\alpha - {\hat\alpha })^ 2+\omega_ 2(\beta -{\hat\beta })^ 2\) is assumed where \(\omega_ 1,\omega_ 2\) are specified nonnegative constants and \({\hat\alpha }\),\({\hat\beta }\) are the least squares estimators of \(\alpha\) and \(\beta\), respectively. Designs symmetric about zero are obtained which minimize the expected loss.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3870431
zbMATH Keywords: squared loss function
zbMATH Keywords: maximum risk among symmetric designs
zbMATH Keywords: robust design
zbMATH Keywords: nearly linear regression
zbMATH Keywords: designs with finite support
zbMATH Keywords: least squares estimators
reviewed by: Hariharan K. Iyer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346406
OpenAlex ID: W1963772992
DOI: 10.1214/AOS/1176346406
description: scientific article; zbMATH DE number 3870431