On Testing for the Nullity of Some Skewness Coefficients

• Published in: International statistical review Vol. 74; no. 1; pp. 47 - 65
• Main Author: Ngatchou-Wandji, Joseph
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01-04-2006; International Statistical Review; Blackwell; International Statistical Institute
• Subjects: Applications; Consistent estimators; Degrees of freedom; Density estimation; Distribution theory; Empirical quantiles; Estimators; Exact sciences and technology; Gaussian distributions; Infinity; Kernel estimator; linebreak Symmetry; Mathematics; Mode estimation; Nonparametric inference; Nonparametric testing; Parametric inference; Perceptron convergence procedure; Probability and statistics; Random variables; Real numbers; Sciences and techniques of general use; Skewed distribution; Skewness; Statistics; Symmetry; Nonparametric testing; Test statistic; Mode estimation; Kernel estimator; Empirical quantiles; Coefficient of skewness; Statistical method; Hypothesis test; Statistical test; Skewness; Skewness measure; Numerical simulation; Test power; Application; Symmetry
• ISSN: 0306-7734; 1751-5823
• DOI: 10.1111/j.1751-5823.2006.tb00160.x

Three tests for the skewness of an unknown distribution are derived for iid data. They are based on suitable normalization of estimators of some usual skewness coefficients. Their asymptotic null distributions are derived. The tests are next shown to be consistent and their power under some sequences of local alternatives is investigated. Their finite sample properties are also studied through a simulation experiment, and compared to those of the $\sqrt{b_{1}}\text{-test}$ . /// Nous construisons trois tests pour l'asymétrie d'une distribution inconnue pour des données iid. Les tests sont basés sur des estimateurs convenablement normalisés des certains coefficients d'asymétrie usuels. La loi asymptotique des statistiques de test est étudiée sous l'hypothèse nulle. La consistance ainsi que la puissance des tests sous des alternatives locales sont étudiées. Les propriétés non asymptotiques des tests sont évaluées au moyen de simulations numériques et comparées à celles du test dit $\sqrt{b_{1}}\text{-test}$ .