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Designs for approximately linear regression: Maximizing the minimum coverage probability of confidence ellipsoids
Author(s) -
Wiens Douglas P.
Publication year - 1993
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 - 10.2307/3315658
Subject(s) - ellipsoid , mathematics , coverage probability , estimator , confidence region , linear regression , statistics , covariance matrix , ellipsoid method , confidence interval , covariance , linear model , regression , geometry , regular polygon , convex optimization , convex combination , physics , astronomy
Abstract The classical D‐optimality principle in regression design may be motivated by a desire to maximize the coverage probability of a fixed‐volume confidence ellipsoid on the regression parameters. When the fitted model is exactly correct, this amounts to minimizing the determinant of the covariance matrix of the estimators. We consider an analogue of this problem, under the approximately linear model E[y|x] = θ T z(x) + f (x). The nonlinear disturbance f (x) is essentially unknown, and the experimenter fits only to the linear part of the response. The resulting bias affects the coverage probability of the confidence ellipsoid on θ. We study the construction of designs which maximize the minimum coverage probability as f varies over a certain class. Explicit designs are given in the case that the fitted response surface is a plane.