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Finite-sample exact tests for linear regressions with bounded dependent variables

Author

Listed:
  • Olivier Gossner

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, LSE - London School of Economics and Political Science)

  • Karl H. Schlag

    (University of Vienna [Vienna])

Abstract

We introduce tests for finite-sample linear regressions with heteroskedastic errors. The tests are exact, i.e., they have guaranteed type I error probabilities when bounds are known on the range of the dependent variable, without any assumptions about the noise structure. We provide upper bounds on probability of type II errors, and apply the tests to empirical data.

Suggested Citation

  • Olivier Gossner & Karl H. Schlag, 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," PSE-Ecole d'économie de Paris (Postprint) halshs-00879792, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00879792
    DOI: 10.1016/j.jeconom.2013.06.003
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    References listed on IDEAS

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    1. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    2. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    3. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2532-2553, November.
    4. Dufour, Jean-Marie & Torres, Olivier, 2000. "Markovian processes, two-sided autoregressions and finite-sample inference for stationary and nonstationary autoregressive processes," Journal of Econometrics, Elsevier, vol. 99(2), pages 255-289, December.
    5. Dufour, J-M. & Hallin, M., 1990. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables , with Statistical Applications," Papers 9104, Universite Libre de Bruxelles - C.E.M.E..
    6. Karl Schlag, 2008. "Exact tests for correlation and for the slope in simple linear regressions without making assumptions," Economics Working Papers 1097, Department of Economics and Business, Universitat Pompeu Fabra.
    7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    8. Xia, Ye, 2008. "Two refinements of the Chernoff bound for the sum of nonidentical Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1557-1559, September.
    9. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    10. Esther Duflo & Michael Kremer & Jonathan Robinson, 2011. "Nudging Farmers to Use Fertilizer: Theory and Experimental Evidence from Kenya," American Economic Review, American Economic Association, vol. 101(6), pages 2350-2390, October.
    11. Karl Schlag, 2008. "A new method for constructing exact tests without making any assumptions," Economics Working Papers 1109, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Elise Coudin & Jean-Marie Dufour, 2009. "Finite-sample distribution-free inference in linear median regressions under heteroscedasticity and non-linear dependence of unknown form," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 19-49, January.
    13. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
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    Citations

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    Cited by:

    1. Frédéric Jouneau-Sion & Olivier Torrès, 2014. "In Fisher's net : exact F-tests in semi-parametric models with exchangeable errors," Working Papers halshs-01062623, HAL.
    2. Ulrich K. Müller, 2020. "A More Robust t-Test," Working Papers 2020-32, Princeton University. Economics Department..
    3. Frédéric Jouneau-Sion & Olivier Torrès, 2014. "In Fisher’s net : exact F-tests in semi-parametric models with exchangeable errors," Working Papers 1422, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    4. Ulrich K. Mueller, 2020. "A More Robust t-Test," Papers 2007.07065, arXiv.org.

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    More about this item

    Keywords

    Nonparametric linear regression; Exact test; Heteroskedasticity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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