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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


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.


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Charles J. Stone. "Admissible Selection of an Accurate and Parsimonious Normal Linear Regression Model." Ann. Statist. 9 (3) 475 - 485, May, 1981.


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

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

Primary: 62J05
Secondary: 62C15

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

Rights: Copyright © 1981 Institute of Mathematical Statistics


Vol.9 • No. 3 • May, 1981
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