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Inference in regression models with many regressors

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  • Anatolyev, Stanislav

Abstract

We investigate the behavior of various standard and modified F, likelihood ratio (LR), and Lagrange multiplier (LM) tests in linear homoskedastic regressions, adapting an alternative asymptotic framework in which the number of regressors and possibly restrictions grows proportionately to the sample size. When the restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared, irrespective of whether there are many or few regressors. However, when the restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The “exact” F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 170 (2012)
Issue (Month): 2 ()
Pages: 368-382

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Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:368-382

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Alternative asymptotic theory; Linear regression; Test size; Test power; F test; Wald test; Likelihood ratio test; Lagrange multiplier test;

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Cited by:
  1. Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
  2. Márcio Laurini, 2012. "Generalized Tests of Investment Fund Performance," IBMEC RJ Economics Discussion Papers 2012-03, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  3. Olivier Ledoit & Michael Wolf, 2013. "Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions," ECON - Working Papers, Department of Economics - University of Zurich 105, Department of Economics - University of Zurich, revised Jul 2013.

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