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VOL. 49 | 2006 The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62064
MathSciNet: MR2338549

Digital Object Identifier: 10.1214/074921706000000518

Primary: 62E15
Secondary: 62F10 , 62F12 , 62J05

Keywords: distribution of post-model-selection estimators , Inference after model selection , linear predictor constructed after model selection , Model selection , model uncertainty , pre-test estimator

Rights: Copyright © 2006, Institute of Mathematical Statistics


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