A-optimal design measures for one-way layouts with additive regression
type: Item
instance of: scholarly article
title: A-optimal design measures for one-way layouts with additive regression
zbMATH Open document ID: 0629.62070
DOI: 10.1016/0378-3758(88)90016-X
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: For linear models with one discrete factor and additive general regression term the problem of characterizing A-optimal design measures for inference on (i) treatment effects, (ii) the regression parameters and (iii) all parameters will be considered. In any of these problems product designs can be found which are optimal among all designs, and equal weight 1/J may be given to each of the J levels of the discrete factor. For problem (i) and (ii) the allocation of the continuous factors for the regression term should follow a suitable optimal design for the corresponding pure regression model, whereas for problem (iii) this would not give an A-optimal product design. For this problem an equivalence theorem for A-optimal product designs will be given. An example will illustrate these results. Finally, by analyzing a model with two discrete factors it will be shown that for enlarged models the best product designs may not be A-optimal.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 62J99
zbMATH DE Number: 4024552
zbMATH Keywords: complete class
zbMATH Keywords: linear models
zbMATH Keywords: one discrete factor
zbMATH Keywords: additive general regression term
zbMATH Keywords: A-optimal design measures
zbMATH Keywords: treatment effects
zbMATH Keywords: product designs
zbMATH Keywords: continuous factors
zbMATH Keywords: equivalence theorem for A-optimal product designs
author: Werner Wierich
MaRDI profile type: Publication
cites work: Optimal and Efficient Designs of Experiments
cites work: Convergent design sequences, for sufficiently regular optimality criteria
cites work: Q4172764
cites work: Q4057438
cites work: On the Nonrandomized Optimality and Randomized Nonoptimality of Symmetrical Designs
cites work: Q3844024
cites work: General equivalence theory for optimum designs (approximate theory)
cites work: Optimale Planung eines Kovarianzanalyse- und eines Intraclass Regressions-Experiments
cites work: Optimal designs for covariates models
cites work: Q3260910
cites work: Q3922026
cites work: Q4768502
cites work: Konkrete optimale Versuchspläne für ein lineares Modell mit einem qualitativen und zwei quantitativen Einflußfaktoren
cites work: On optimal designs and complete class theorems for experiments with continuous and discrete factors of influence
Recommended article: Optimal designs for a one-way layout with covariates
Recommended article: Optimal Designs for Additive Linear Models
Recommended article: A-optimal designs for an additive cubic model
Recommended article: An algorithm for A-optimal regression designs
Recommended article: Optimal design for additive partially nonlinear models
Recommended article: On the efficiency of a semiparametric approach to the one-way layout
Recommended article: Q5257322
description: scientific article; zbMATH DE number 4024552