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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.

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Hannes Leeb. 2006-11-07. The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations. https://doi.org/10.1214/074921706000000518

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