Minimax D-optimal designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, the minimax D-optimal design problem has an objective function as a difference of two convex functions. An effective algorithm is developed to compute minimax D-optimal designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax D-optimal designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax D-optimal designs. / Graduate
Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/12863 |
Date | 20 April 2021 |
Creators | Yzenbrandt, Kai |
Contributors | Zhou, Julie |
Source Sets | University of Victoria |
Language | English, English |
Detected Language | English |
Type | Thesis |
Format | application/pdf |
Rights | Available to the World Wide Web |
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