D-optimal designs for polynomial regression with exponential weight function

Weighted polynomial regression with exponential weight function on an interval is considered. The D -optimal designs are completely characterized via three differential equations. Some invariant properties of the optimal designs under affine transformation are derived. The optimal design as degree o...

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Published in:Metrika 2009-11, Vol.70 (3), p.339-354
Main Authors: Chang, Fu-Chuen, Chang, Hsiu-Ching, Wang, Sheng-Shian
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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description Weighted polynomial regression with exponential weight function on an interval is considered. The D -optimal designs are completely characterized via three differential equations. Some invariant properties of the optimal designs under affine transformation are derived. The optimal design as degree of polynomial goes to infinity, is shown to converge weakly to the arcsin distribution. Comparisons of the optimal designs with the arcsin distribution are also made.
doi_str_mv 10.1007/s00184-008-0195-2
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subjects Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
title D-optimal designs for polynomial regression with exponential weight function
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