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

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  • Gossner, Olivier
  • Schlag, Karl H.

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

  • Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
  • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:75-84
    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. 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.
    3. 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.
    4. 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..
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    10. 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.
    11. Karl H. Schlag, 2006. "Designing Non-Parametric Estimates and Tests for Means," Economics Working Papers ECO2006/26, European University Institute.
    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.
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    More about this item

    Keywords

    Nonparametric linear regression; Exact test; Heteroskedasticity;

    JEL classification:

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

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