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Testing for normality in linear regression models using regression and scale equivariant estimators

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  • Tabri, Rami Victor
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    Abstract

    In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.

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    Bibliographic Info

    Article provided by Elsevier in its journal Economics Letters.

    Volume (Year): 122 (2014)
    Issue (Month): 2 ()
    Pages: 192-196

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    Handle: RePEc:eee:ecolet:v:122:y:2014:i:2:p:192-196

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

    Related research

    Keywords: Normality test; Linear regression; Regression and scale equivariant estimators; Monte Carlo test;

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    1. Jean-Marie Dufour, 2005. "Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics," CIRANO Working Papers 2005s-02, CIRANO.
    2. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1500-1529, December.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Stinchcombe, Maxwell B & White, Halbert, 1992. "Some Measurability Results for Extrema of Random Functions over Random Sets," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 495-514, July.
    5. Onder, A. Ozlem & Zaman, Asad, 2005. "Robust tests for normality of errors in regression models," Economics Letters, Elsevier, vol. 86(1), pages 63-68, January.
    6. Breusch, Trevor S., 1980. "Useful invariance results for generalized regression models," Journal of Econometrics, Elsevier, vol. 13(3), pages 327-340, August.
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