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Tests multiples simulés et tests de normalité basés sur plusieurs moments dans les modèles de régression

Author

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  • DUFOUR, Jean-Marie
  • FARHAT, Abdeljelil
  • KHALAF, Lynda

Abstract

This paper illustrates the usefulness of resampling based methods in the context of multiple (simultaneous) tests, with emphasis on econometric applications. Economic theory often suggests joint (or simultaneous) hypotheses on econometric models; consequently, the problem of evaluating joint rejection probabilities arises frequently in econometrics and statistics. In this regard, it is well known that ignoring the joint nature of multiple hypotheses may lead to serious test size distortions. Whereas most available multiple test techniques are conservative in the presence of non-independent statistics, our proposed tests provably achieve size control. Specifically, we use the Monte Carlo (MC) test technique to extend several well known combination methods to the non-independent statistics contexts. We first cast the multiple test problem into a unified statistical framework which: (i) serves to show how exact global size control is achieved through the MC test method, and (ii) yields a number of superior tests previously not considered. Secondly, we provide a review of relevant available results. Finally, we illustrate the applicability of our proposed procedure to the problem of moments-based normality tests. For this problem, we propose an exact variant of Kiefer and Salmon’s (1983) test, and an alternative combination method which exploits the well known Fisher-Pearson procedure. Our simulation study reveals that the latter method seems to correct for the problem of test biases against platikurtic alternatives. In general, our results show that concrete and non-spurious power gains (over standard combination methods) can be achieved through our multiple Monte Carlo test approach.

Suggested Citation

  • DUFOUR, Jean-Marie & FARHAT, Abdeljelil & KHALAF, Lynda, 2005. "Tests multiples simulés et tests de normalité basés sur plusieurs moments dans les modèles de régression," Cahiers de recherche 07-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:07-2005
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    References listed on IDEAS

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    1. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    3. Bera, Anil K. & Jarque, Carlos M., 1982. "Model specification tests : A simultaneous approach," Journal of Econometrics, Elsevier, vol. 20(1), pages 59-82, October.
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    Cited by:

    1. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    2. Jean-Marie DUFOUR & Lynda KHALAF & Marcel VOIA, 2013. "Finite-Sample Resampling-Based Combined Hypothesis Tests, with Applications to Serial Correlation and Predictability," Cahiers de recherche 13-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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    More about this item

    Keywords

    linear regression; normality test; goodness of fit; skewness; kurtosis; higher moments; Monte Carlo; induced test; test combination; simultaneous inference; Tippett; Fisher; Pearson; SURE; heteroskedasticity test;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • 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
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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