Open Access
Translator Disclaimer
May, 1981 Admissible Selection of an Accurate and Parsimonious Normal Linear Regression Model
Charles J. Stone
Ann. Statist. 9(3): 475-485 (May, 1981). DOI: 10.1214/aos/1176345452

Abstract

Let $M_0$ be a normal linear regression model and let $M_1,\cdots, M_K$ be distinct proper linear submodels of $M_0$. Let $\hat k \in \{0,\cdots, K\}$ be a model selection rule based on observed data from the true model. Given $\hat k$, let the unknown parameters of the selected model $M_{\hat k}$ be fitted by the maximum likelihood method. A loss function is introduced which depends additively on two parts: (i) a measure of the difference between the fitted model $M_{\hat k}$ and the true model; and (ii) a measure $C_{\hat k}$ of the "complexity" of the selected model. A natural model selection rule $\bar{k}$, which minimizes an empirical version of this loss, is shown to be admissible and very nearly Bayes.

Citation

Download Citation

Charles J. Stone. "Admissible Selection of an Accurate and Parsimonious Normal Linear Regression Model." Ann. Statist. 9 (3) 475 - 485, May, 1981. https://doi.org/10.1214/aos/1176345452

Information

Published: May, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0499.62056
MathSciNet: MR615424
Digital Object Identifier: 10.1214/aos/1176345452

Subjects:
Primary: 62J05
Secondary: 62C15

Keywords: Admissibility , Complexity , generalized Bayes , normal linear regression model , parsimony

Rights: Copyright © 1981 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.9 • No. 3 • May, 1981
Back to Top