Institute of Mathematical Statistics Lecture Notes - Monograph Series

The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations

Hannes Leeb

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Abstract

We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We then analyze the large-sample limit behavior of these cdfs, in the fixed-parameter case and under local alternatives.

Chapter information

Source
Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 291-311

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196283967

Digital Object Identifier
doi:10.1214/074921706000000518

Mathematical Reviews number (MathSciNet)
MR2338549

Zentralblatt MATH identifier
1268.62064

Subjects
Primary: 62E15: Exact distribution theory
Secondary: 62F10: Point estimation 62F12: Asymptotic properties of estimators 62J05: Linear regression

Keywords
model uncertainty model selection inference after model selection distribution of post-model-selection estimators linear predictor constructed after model selection pre-test estimator

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Leeb, Hannes. The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations. Optimality, 291--311, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000518. https://projecteuclid.org/euclid.lnms/1196283967


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