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Further Results on Minimax Designs to Estimate the Slope of a Response Surface
Author(s) -
Huda Shahariar
Publication year - 1990
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710320209
Subject(s) - minimax , mathematics , optimal design , minification , limiting , polynomial , polynomial and rational function modeling , polynomial regression , surface (topology) , regression , mathematical optimization , statistics , mathematical analysis , geometry , mechanical engineering , engineering
The problem considered is polynomial regression and minimization of the variance of estimated slope maximized over all points in the region of interest when the design region and region of interest are hyperspheres with a common centre. Optimal designs under the criterion are derived for the second‐order model. Method of deriving optimal designs for the third‐order model is indicated and some limiting results on these designs are obtained.