An empirical Bayes approach to polynomial regression under order restrictions

Leonard W. Deaton, Fleet Analysis Center, Naval Weapons Station, Seal Beach, California

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Copyright © 1980 Oxford University Press. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review.

Abstract

An unknown polynomial is to be estimated over a finite interval from N independent, normally distributed observations. A prior distribution is placed on the polynomial coefficients expressing the opinion that the coefficients decrease in absolute value as the degree of the corresponding terms increase. The data are used to estimate the parameters in the prior distribution of the coefficients. A Monte Carlo study is presented which compares the proposed method with the lack-of-fit procedure. This study indicates that the proposed method performs well in terms of minimizing a squared error loss as well as in yielding the correct degree of the polynomial being estimated.