D-optimal designs for full and reduced Fourier regression models

D-optimal designs for full and reduced Fourier regression models The optimal designs for Fourier regression models under the D-optimality criterion are discussed in this article. First, we investigate the D-optimal designs for estimating two coefficients corresponding to either sine or cosine terms in a full Fourier regression model. In many biological applications, estimating such specific pairs of coefficients is of interest. As a result of this article, the D-optimal designs for estimating these “coefficient pairs” can be constructed either explicitly or numerically for Fourier regression models with any order. Our resulting designs are provided for Fourier regression models with order less than 6. Secondly, we discuss the sensitivity of our resulting optimal designs for a full Fourier regression model when the true model is actually a reduced version of the assumed one. Lastly, we provide the algorithm for obtaining the D-optimal designs for a reduced Fourier regression model and the D-optimal designs for a useful reduced Fourier model are constructed. The comparison study shows that the constructed designs incorporating the reduced model are efficient. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Papers Springer Journals

D-optimal designs for full and reduced Fourier regression models

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research/Decision Theory
ISSN
0932-5026
eISSN
1613-9798
D.O.I.
10.1007/s00362-015-0727-6
Publisher site
See Article on Publisher Site

Abstract

The optimal designs for Fourier regression models under the D-optimality criterion are discussed in this article. First, we investigate the D-optimal designs for estimating two coefficients corresponding to either sine or cosine terms in a full Fourier regression model. In many biological applications, estimating such specific pairs of coefficients is of interest. As a result of this article, the D-optimal designs for estimating these “coefficient pairs” can be constructed either explicitly or numerically for Fourier regression models with any order. Our resulting designs are provided for Fourier regression models with order less than 6. Secondly, we discuss the sensitivity of our resulting optimal designs for a full Fourier regression model when the true model is actually a reduced version of the assumed one. Lastly, we provide the algorithm for obtaining the D-optimal designs for a reduced Fourier regression model and the D-optimal designs for a useful reduced Fourier model are constructed. The comparison study shows that the constructed designs incorporating the reduced model are efficient.

Journal

Statistical PapersSpringer Journals

Published: Dec 29, 2015

References

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