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December, 1984 Bootstrap and Cross-Validation Estimates of the Prediction Error for Linear Regression Models
Olaf Bunke, Bernd Droge
Ann. Statist. 12(4): 1400-1424 (December, 1984). DOI: 10.1214/aos/1176346800


Different estimates of the mean squared error of prediction for linear regression models are derived by the bootstrap and cross-validation approaches. A comparison is made under normal error distributions, especially by the biases and the mean square errors. The results indicate that the bias corrected bootstrap estimator is best unbiased and should be the first choice, while its simulated variant has approximately the same behaviour. On the other hand, if only a comparison between uncorrected estimators is made (with implications for nonlinear regression models in mind), then other variants of bootstrap estimates are preferable for a large or a small dimension of the model parameter. For a small dimension, the cross-validation estimate and sometimes grouped variants of it seem also to be acceptable if the model error is known to be small.


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Olaf Bunke. Bernd Droge. "Bootstrap and Cross-Validation Estimates of the Prediction Error for Linear Regression Models." Ann. Statist. 12 (4) 1400 - 1424, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0557.62039
MathSciNet: MR760696
Digital Object Identifier: 10.1214/aos/1176346800

Primary: 62G05
Secondary: 62J05

Keywords: bootstrap approach , cross-validation , Linear regression , Model selection , prediction error

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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