The Annals of Mathematical Statistics

The Choice of the Degree of a Polynomial Regression as a Multiple Decision Problem

T. W. Anderson

Full-text: Open access

Abstract

On the basis of a sample of observations, an investigator wants to determine the appropriate degree of a polynomial in the index, say time, to represent the regression of the observable variable. This multiple decision problem is formulated in terms used in the theory of testing hypotheses. Given the degree of polynomial regression, the probability of deciding a higher degree is specified and does not depend on what the actual polynomial is (expect its degree). Within the class of procedures satisfying these conditions and symmetry (or two-sidedness) conditions, the probabilities of correct decisions are maximized. The optimal procedure is to test in sequence whether coefficients are 0, starting with the highest (specified) degree. The procedure holds for other linear regression functions when the independent variates are ordered. The problem and its solution can be generalized to the multivariate case and to other cases with a certain structure of sufficient statistics.

Article information

Source
Ann. Math. Statist., Volume 33, Number 1 (1962), 255-265.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704729

Digital Object Identifier
doi:10.1214/aoms/1177704729

Mathematical Reviews number (MathSciNet)
MR148180

Zentralblatt MATH identifier
0124.09304

JSTOR
links.jstor.org

Citation

Anderson, T. W. The Choice of the Degree of a Polynomial Regression as a Multiple Decision Problem. Ann. Math. Statist. 33 (1962), no. 1, 255--265. doi:10.1214/aoms/1177704729. https://projecteuclid.org/euclid.aoms/1177704729


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