## The Annals of Statistics

- Ann. Statist.
- Volume 9, Number 3 (1981), 475-485.

### Admissible Selection of an Accurate and Parsimonious Normal Linear Regression Model

#### 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.

#### Article information

**Source**

Ann. Statist., Volume 9, Number 3 (1981), 475-485.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345452

**Digital Object Identifier**

doi:10.1214/aos/1176345452

**Mathematical Reviews number (MathSciNet)**

MR615424

**Zentralblatt MATH identifier**

0499.62056

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62J05: Linear regression

Secondary: 62C15: Admissibility

**Keywords**

Admissibility normal linear regression model generalized Bayes parsimony complexity

#### Citation

Stone, Charles J. Admissible Selection of an Accurate and Parsimonious Normal Linear Regression Model. Ann. Statist. 9 (1981), no. 3, 475--485. doi:10.1214/aos/1176345452. https://projecteuclid.org/euclid.aos/1176345452