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August 2000 On the degrees of freedom in shape-restricted regression
Mary Meyer, Michael Woodroofe
Ann. Statist. 28(4): 1083-1104 (August 2000). DOI: 10.1214/aos/1015956708

Abstract

For the problem of estimating a regression function, $\mu$ say, subject to shape constraints, like monotonicity or convexity, it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. These generalize equalities from the case of linear regression. As an application, it is shown that the maximum likelihood estimator of the error variance $\sigma^2$ is asymptotically normal with mean $\sigma^2$ and variance $2\sigma_2/n$. For monotone regression, it is shown that the maximum likelihood estimator of $\mu$ attains the optimal rate of convergence, and a bias correction to the maximum likelihood estimator of $\sigma^2$ is derived.

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Mary Meyer. Michael Woodroofe. "On the degrees of freedom in shape-restricted regression." Ann. Statist. 28 (4) 1083 - 1104, August 2000. https://doi.org/10.1214/aos/1015956708

Information

Published: August 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62340
MathSciNet: MR1810920
Digital Object Identifier: 10.1214/aos/1015956708

Subjects:
Primary: 62G08

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 4 • August 2000
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