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Robust sequential designs for approximately linear models
Author(s) -
Wiens Douglas P.
Publication year - 1996
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 - 10.2307/3315690
Subject(s) - sequential analysis , mathematics , linear model , optimal design , design of experiments , variance (accounting) , linear regression , term (time) , algorithm , function (biology) , computer science , mathematical optimization , sample size determination , design matrix , statistics , physics , accounting , quantum mechanics , evolutionary biology , business , biology
We consider the problem of the sequential choice of design points in an approximately linear model. It is assumed that the fitted linear model is only approximately correct, in that the true response function contains a nonrandom, unknown term orthogonal to the fitted response. We also assume that the parameters are estimated by M ‐estimation. The goal is to choose the next design point in such a way as to minimize the resulting integrated squared bias of the estimated response, to order n ‐1 . Explicit applications to analysis of variance and regression are given. In a simulation study the sequential designs compare favourably with some fixed‐sample‐size designs which are optimal for the true response to which the sequential designs must adapt.