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The distribution of a linear predictor after model selection: unconditional finite-sample distributions and asymptotic approximations. (English) Zbl 1268.62064

Rojo, Javier (ed.), Optimality. The second Erich L. Lehmann symposium. Selected papers based on the presentations at the symposium, Houston, TX, USA, May 19–22, 2004. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-66-9/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 49, 291-311 (2006).
Summary: 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.
For the entire collection see [Zbl 1113.62002].

MSC:

62J05 Linear regression; mixed models
62M20 Inference from stochastic processes and prediction
62E20 Asymptotic distribution theory in statistics
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