| Title: |
Explicit Fourth Order Generalized Jarque-Bera Tests And Applications To Recent Laws. |
| Authors: |
Onesiphore Da, Gandasor Bonyiri; Gning, Gorgui; Ngom, Modou |
| Source: |
Afrika Statistika; Jul2023, Vol. 18 Issue 3, p3551-3566, 16p |
| Subject Terms: |
CHI-squared test; GAUSSIAN distribution; ECONOMETRICS; COMPUTER software; ASYMPTOTIC distribution |
| Abstract (English): |
The jarque-Bera chi-square test is one of the most iconic and celebrated tests of normality. It is overwhelmingly used in many disciplines, especially in Econometrics and related software. Typically, a precise combination of the squared deviations of the empirical kurtotis and the empirical skewness from their true counterparts was proved by Jarque and Bera (1987) to be asymptotically approximated to a chi-square law of two degrees of freedom. The then-derived Jarque-Bera test has been devised from that weal limit. As we will check it again, it proved itself very efficient to detect normality even for single digit values of the sample size. Now, the use of the functional empirical process made it possible to have remarkable expansions of statistics including empirical moments. Thus allows to extend the asymptotic theory of the Jarque-Bera (JB) Statistic beyond the normality context and the possibility of using reduced moments of order more than three and four. The study shed light of coefficients of the classical JB statistics paving the way to obtaining generalized tests for fitting arbitrary distributions whenever the finiteness of moments allows it. [ABSTRACT FROM AUTHOR] |
| Abstract (French): |
Le test de Jarque-Bera a été spécifiquement conçu pour tester la normalité des données et repose naturellement sur les paramètres d'asymétrie et d'applatissement. Dans cette discussion, nous verrons que ce test nécessite en réalité la finitude des huit premiers moments. De plus, en utilisant le processus empirique fonctionnel, nous généraliserons ce test pour ajuster n'importe quelle distribution ayant au moins huit premiers moments finis, ce qui donne naissance aux tests Jarque-Bera généralisés (GJBT). Une étude de simulation sur l'efficacité des GJBT est présentée. De nouvelles pistes de recherche sont recommandées. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |