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Bayesian and maximin optimal designs for heteroscedastic regression models
Author(s) -
Dette Holger,
Haines Linda M.,
Imhof Lorens A.
Publication year - 2005
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550330205
Subject(s) - minimax , polynomial regression , mathematics , optimal design , heteroscedasticity , bayesian probability , mathematical optimization , polynomial , regression analysis , computer science , statistics , mathematical analysis
The authors consider the problem of constructing standardized maximin D ‐optimal designs for weighted polynomial regression models. In particular they show that by following the approach to the construction of maximin designs introduced recently by Dette, Haines & Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian q ‐optimal designs. They further demonstrate that the results are more broadly applicable to certain families of nonlinear models. The authors examine two specific weighted polynomial models in some detail and illustrate their results by means of a weighted quadratic regression model and the Bleasdale–Nelder model. They also present a capstone example involving a generalized exponential growth model.