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Marginally restricted sequential D‐optimal designs
Author(s) -
LópezFidalgo Jesús,
MartínMartín Raul,
Wiens Douglas P.
Publication year - 2008
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.5550360305
Subject(s) - a priori and a posteriori , mathematical optimization , mathematics , set (abstract data type) , variable (mathematics) , optimal design , value (mathematics) , sequential analysis , computer science , algorithm , statistics , mathematical analysis , philosophy , epistemology , programming language
In many experiments, not all explanatory variables can be controlled. When the units arise sequentially, different approaches may be used. The authors study a natural sequential procedure for “marginally restricted” D‐optimal designs. They assume that one set of explanatory variables (x 1 ) is observed sequentially, and that the experimenter responds by choosing an appropriate value of the explanatory variable x 2 . In order to solve the sequential problem a priori, the authors consider the problem of constructing optimal designs with a prior marginal distribution for x 1 . This eliminates the influence of units already observed on the next unit to be designed. They give explicit designs for various cases in which the mean response follows a linear regression model; they also consider a case study with a nonlinear logistic response. They find that the optimal strategy often consists of randomizing the assignment of the values of x 2 .