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Size-Dependent Probability Bounds for t-Tests

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  • Alessandro Palandri

Abstract

The paper extends Chebyshev’s inequality to incorporate moments’ convergence in t-tests of model parameters. Size-dependent probability bounds are derived from one conditional higher-order moment of the distribution of the test statistic. Monte Carlo simulations attest that, in the cases of heteroskedastic and autocorrelated observations, the proposed bounds over-reject less than the asymptotic approximation and bootstrap methods. Therefore, when asymptotic critical values are suspected to lead to the over-rejection of the null hypothesis, the proposed inequalities may be used in conjunction to bootstrap methods to reduce the number of instances in which multiple re-samplings and associated estimations have to be performed.JEL classiï¬ cation numbers: C01, C12, C15. Keywords: Chebyshev’s Inequality, Asymptotic Approximation, Over Rejection, Bootstrap, Wild Bootstrap.

Suggested Citation

  • Alessandro Palandri, 2020. "Size-Dependent Probability Bounds for t-Tests," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 9(3), pages 1-1.
    • Handle: RePEc:spt:stecon:v:9:y:2020:i:3:f:9_3_1
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    References listed on IDEAS

    as
    1. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    2. 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.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
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    More about this item

    Keywords

    chebyshev’s inequality; asymptotic approximation; over rejection; bootstrap; wild bootstrap.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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