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

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

2006-11-07

arxiv.org/abs/math/0611186v1

IMS Lecture Notes--Monograph Series 2006, Vol. 49, 291-311

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000518 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000518

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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