Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 1, 90--105

$c$-optimal Designs for Weighted Polynomial Models


Mong-Na Lo Huang, National Sun Yat-Sen University, Kaohsiung, Taiwan
Ray-Bing Chen, National University of Kaohsiung, Kaohsiung, Taiwan
Ying-Ying Chen, National Sun Yat-Sen University, Kaohsiung, Taiwan

SUMMARY. $c$-optimal design problems for weighted polynomial models are discussed. Vectors $c$, where $c$-optimal designs are supported by some extreme points of a certain equioscillating function, are characterized, and this equioscillating function is a linear combination of the regression functions. These results are then applied to the no-intercept model in which the optimal designs for estimating certain individual parameters can be found. Examples of applications of the above results in finding locally $c$-optimal designs for some nonlinear models are discussed. Finally the results are extended to a more general linear model.

AMS (1991) subject classification. 62K05.

Key words and phrases. Alternating extreme point, equioscillating function, individual regression coefficient, weak Chebyshev system.

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