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Designs of experiments in a polynomial regression when there is uncertainty about the degree
Author(s) -
Dette Holger
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19990791317
Subject(s) - degree (music) , polynomial regression , mathematics , polynomial , set (abstract data type) , sequence (biology) , regression , sample (material) , regression analysis , statistics , mathematical optimization , computer science , mathematical analysis , physics , chemistry , chromatography , biology , acoustics , genetics , programming language
If an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations, Anderson (1962) showed that the following method is optimal. Starting with the highest (specified) degree the procedure is to test in sequence whether the coefficients are 0. In this paper optimal designs for Anderson's procedure are described explicitly. The optimal design maximizes the minimum power of a given set of alternatives.