The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations
Hannes Leeb
Source: Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006) , 291-311.
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.
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Primary Subjects: 62E15
Secondary Subjects: 62F10, 62F12, 62J05
Keywords: model uncertainty; model selection; inference after model selection; distribution of post-model-selection estimators; linear predictor constructed after model selection; pre-test estimator
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196283967
Digital Object Identifier: doi:10.1214/074921706000000518
Institute of Mathematical Statistics Lecture Notes - Monograph Series
