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

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  • Hannes Leeb

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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File URL: http://arxiv.org/pdf/math/0611186
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number math/0611186.

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Date of creation: Nov 2006
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Publication status: Published in IMS Lecture Notes--Monograph Series 2006, Vol. 49, 291-311
Handle: RePEc:arx:papers:math/0611186

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Web page: http://arxiv.org/

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  1. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
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Cited by:
  1. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation for Research in Economics, Yale University.
  2. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  3. Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.

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