Compromise designs in heteroscedastic linear models
type: Item
instance of: scholarly article
title: Compromise designs in heteroscedastic linear models
zbMATH Open document ID: 0766.62043
DOI: 10.1016/0378-3758(92)90017-M
author: Anirban DasGupta
author: Saurabh Mukhopadhyay
author: William J. Studden
published in: Journal of Statistical Planning and Inference
publication date: 1993-01-16T00:00:00Z
review text: The authors restrict themselves to heteroscedastic linear models (as opposed to homoscedastic models) in which the variance of a response is an exponential or a power function of its mean. The solution to the dilemma of the experimenter who is on one hand interested in many estimation problems and, at the same time, would like to have a design with an efficiency of at least \(1/(1+\varepsilon)\) for each problem is resolved through `compromise designs'. This discussion is carried out for both classical as well as Bayes problems. The variance function and its effect on smallest \(\varepsilon\) is examined, and the maximin efficient design is then compared to the usual \(A\)-optimal design.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 95638
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: canonical moments
zbMATH Keywords: polynomial regressions
zbMATH Keywords: linear regression
zbMATH Keywords: compromise designs
zbMATH Keywords: \(A\)-optimal design
zbMATH Keywords: heteroscedastic linear models
zbMATH Keywords: variance function
zbMATH Keywords: maximin efficient design
reviewed by: D. V. Chopra
MaRDI profile type: Publication
cites work: Using residuals robustly I: Tests for heteroscedasticity, nonlinearity
cites work: Correcting Inhomogeneity of Variance with Power Transformation Weighting
cites work: Robust estimation in heteroscedastic linear models
cites work: Optimal Bayesian experimental design for linear models
cites work: An optimization problem with applications to optimal design theory
cites work: Q3217425
cites work: Q3747504
cites work: Robust Bayesian experimental designs in normal linear models
cites work: Minimax risk over hyperrectangles, and implications
cites work: Limiting the Risk of Bayes and Empirical Bayes Estimators--Part I: The Bayes Case
cites work: Limiting the Risk of Bayes and Empirical Bayes Estimators--Part II: The Empirical Bayes Case
cites work: Optimum Allocation in Linear Regression Theory
cites work: Q5676896
cites work: Efficiency Problems in Polynomial Estimation
cites work: Least Squares Estimation when the Covariance Matrix and Parameter Vector are Functionally Related
cites work: Optimal Experimental Designs
cites work: General equivalence theory for optimum designs (approximate theory)
cites work: Optimal designs for large degree polynomial regression
cites work: D-optimal designs on the unit \(q\)-ball
cites work: Q4164707
cites work: Constrained optimal designs
cites work: Robust bayes and minimax-bayes estimation design in linear regression1
cites work: Q3727167
cites work: General differential and Lagrangian theory for optimal experimental design
cites work: Estimation of parameters in a linear model
cites work: Q3857549
cites work: The range of the (n + 1)th moment for distributions on [0, 1]
cites work: Extreme nth moments for distributions on [0, 1] and the inverse of a moment space map
cites work: Some Striking Properties of Binomial and Beta Moments
cites work: Principal representations and canonical moment sequences for distributions on an interval
cites work: \(D_s\)-optimal designs for polynomial regression using continued fractions
cites work: Some Robust-Type D-Optimal Designs in Polynomial Regression
cites work: Q3692655
cites work: Note on some \(\phi _ p\)-optimal designs for polynomial regression
full work available at URL: 0378-3758(92)90017-m
OpenAlex ID: W2084873677
description: scientific article; zbMATH DE number 95638