The Annals of Statistics

Optimal Designs for Identifying the Degree of a Polynomial Regression

Holger Dette

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Abstract

If an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations, Anderson 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 determined explicitly. The optimal design maximizes the minimum power of a given set of alternatives.

Article information

Source
Ann. Statist., Volume 23, Number 4 (1995), 1248-1266.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324708

Digital Object Identifier
doi:10.1214/aos/1176324708

Mathematical Reviews number (MathSciNet)
MR1353505

Zentralblatt MATH identifier
0847.62064

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs

Keywords
Testing the degree of a polynomial regression minimax designs Chebyshev polynomials canonical moments locally optimal designs

Citation

Dette, Holger. Optimal Designs for Identifying the Degree of a Polynomial Regression. Ann. Statist. 23 (1995), no. 4, 1248--1266. doi:10.1214/aos/1176324708. https://projecteuclid.org/euclid.aos/1176324708


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