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Title: New tests of multivariate normality by a characterizing property of the Hermite operator Authors:  Bruno Ebner - Karlsruhe Institute of Technology (Germany) [presenting]
Norbert Henze - Karlsruhe institute of Technology (Germany)
Abstract: A novel class of affine invariant tests for normality in any dimension is proposed. The starting point is a characterization of multivariate normality by a partial differential equation motivated by the Hermite operator and its eigenfunctions. The test statistic thus uses the second partial derivative of the empirical characteristic function. Weak convergence results under the null, under fixed and under contiguous alternatives are derived. A finite sample Monte Carlo simulation study shows that the new statistic outperforms most of the well established procedures.