Minimax designs for estimating slopes in a trigonometric regression model

Abstract

Designs for the first order trigonometric regression model over an interval on the real line are considered for the situation where estimation of the slope of the response surface at various points in the factor space is of primary interest. Minimization of the variance of the estimated slope at a point maximized over all points in the region of interest is taken as the design criterion. Optimal designs under the minimax criterion are derived for the situation where the design region and the region of interest are identical and a symmetric “partial cycle”. Some comparisons of the minimax designs with the traditional D- and A-optimal designs are provided. Efficiencies of some exact designs under the minimax criterion are also investigated.

Keywords:

• D-optimal designs
• minimax designs
• response surface designs
• trigonometric regression

AMS Subject Classification:

• 62K20
• 62K05
• 62K99

Additional information

Funding

This research was supported by Kuwait University Research Administration under Research Grant SS02/17. The authors are grateful to the referee for a thorough review and very helpful comments which substantially improved the article.