Robust designs for approximately linear regression: \(M\)-estimated parameters
type: Item
instance of: scholarly article
title: Robust designs for approximately linear regression: \(M\)-estimated parameters
zbMATH Open document ID: 0807.62056
DOI: 10.1016/0378-3758(94)90147-3
author: Douglas P. Wiens
published in: Journal of Statistical Planning and Inference
publication date: 1994-07-12T00:00:00Z
review text: The author considers a parameter-linear regression model \(y_ i= \Theta^ T u(x_ i)+ f(x_ i)+ \varepsilon_ i\), \(i=1, \dots, n\); with model contamination \(f(x_ i)\). Usually, robustness of estimation and design robustness against model deviations are considered separately. An advantage of the paper under review is that it presents a common approach: For Huber's \(M\)-estimators and parametric contamination \(f_ \alpha(x):= \alpha^ T \nu(x)\) with given \(\nu(x)\), the author investigates the designing problem where as loss function a sum of asymptotic variances, bias and model misspecification is used. Especially minimax rotatable designs are derived for multiple linear regression with quadratic contamination, subject to a lower bound on the power of a robust test of the hypothesis \(\alpha=0\). The optimal designs place their mass at the centre of the design space, and on a sphere interior to the design space.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 605339
zbMATH Keywords: robustness of estimation
zbMATH Keywords: design robustness against model deviations
zbMATH Keywords: Huber's \(M\)-estimators
zbMATH Keywords: parametric contamination
zbMATH Keywords: sum of asymptotic variances, bias and model misspecification
zbMATH Keywords: minimax rotatable designs
zbMATH Keywords: multiple linear regression
zbMATH Keywords: quadratic contamination
zbMATH Keywords: robust test
reviewed by: Wolfgang Näther
MaRDI profile type: Publication
full work available at URL: 0378-3758(94)90147-3
OpenAlex ID: W1976132351
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description: scientific article; zbMATH DE number 605339