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


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  • Jean-Marie Dufour


  • Abdeljelil Farhat
  • Lynda Khalaf


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. Cet article illustre l’applicabilité des méthodes de rééchantillonnage dans le cadre des tests multiples (simultanés), pour divers problèmes économétriques. Les hypothèses simultanées sont une conséquence habituelle de la théorie économique, de sorte que le contrôle de la probabilité de rejet de combinaisons de tests est un problème que l’on rencontre fréquemment dans divers contextes économétriques et statistiques. À ce sujet, on sait que le fait d’ignorer le caractère conjoint des hypothèses multiples peut faire en sorte que le niveau de la procédure globale dépasse considérablement le niveau désiré. Alors que la plupart des méthodes d’inférence multiple sont conservatrices en présence de statistiques non indépendantes, les tests que nous proposons visent à contrôler exactement le niveau de signification. Pour ce faire, nous considérons des critères de test combinés proposés initialement pour des statistiques indépendantes. En appliquant la méthode des tests de Monte Carlo, nous montrons comment ces méthodes de combinaison de tests peuvent s’appliquer à de tels cas, sans recours à des approximations asymptotiques. Après avoir passé en revue les résultats antérieurs sur ce sujet, nous montrons comment une telle méthodologie peut être utilisée pour construire des tests de normalité basés sur plusieurs moments pour les erreurs de modèles de régression linéaires. Pour ce problème, nous proposons une généralisation valide à distance finie du test asymptotique proposé par Kiefer et Salmon (1983) ainsi que des tests combinés suivant les méthodes de Tippett et de Pearson-Fisher. Nous observons empiriquement que les procédures de test corrigées par la méthode des tests de Monte Carlo ne souffrent pas du problème de biais (ou sous-rejet) souvent rapporté dans cette littérature – notamment contre les lois platikurtiques – et permettent des gains sensibles de puissance par rapport aux méthodes combinées usuelles.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2005s-05.

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Date of creation: 01 Feb 2005
Date of revision:
Handle: RePEc:cir:cirwor:2005s-05

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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; régression linéaire; test de normalité; ajustement; asymétrie; aplatissement; moments d’ordre supérieur; Monte Carlo; test induit; combinaison de tests; inférence simultanée; Tippett; Fisher; Pearson; SURE; test d’hétéroscédasticité;

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Cited by:
  1. Jean-Marie Dufour & Lynda Khalaf & Marcel Voia, 2013. "Finite-sample resampling-based combined hypothesis tests, with applications to serial correlation and predictability," CIRANO Working Papers 2013s-40, CIRANO.


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