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

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  • Tabri, Rami Victor

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.

Suggested Citation

  • Tabri, Rami Victor, 2014. "Testing for normality in linear regression models using regression and scale equivariant estimators," Economics Letters, Elsevier, vol. 122(2), pages 192-196.
    • Handle: RePEc:eee:ecolet:v:122:y:2014:i:2:p:192-196
    DOI: 10.1016/j.econlet.2013.11.017
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    1. Maxwell B. Stinchcombe & Halbert White, 1992. "Some Measurability Results for Extrema of Random Functions Over Random Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 495-514.
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    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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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    More about this item

    Keywords

    Normality test; Linear regression; Regression and scale equivariant estimators; Monte Carlo test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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