
Testing normality in any dimension by Fourier methods in a multivariate Stein equation
We study a novel class of affine invariant and consistent tests for mult...
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Testing for normality in any dimension based on a partial differential equation involving the moment generating function
We use a system of firstorder partial differential equations that chara...
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Tests for multivariate normality – a critical review with emphasis on weighted L^2statistics
This article gives a synopsis on new developments in affine invariant te...
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A new test of multivariate normality by a double estimation in a characterizing PDE
This paper deals with testing for nondegenerate normality of a dvariate...
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More good news on the (only) affine invariant test for multivariate reflected symmetry about an unknown center
We revisit the problem of testing for multivariate reflected symmetry ab...
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Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives in Random Bernoulli Sequences
We study a class of tests of the randomness of Bernoulli sequences and t...
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On the feasibility of parsimonious variable selection for Hotelling's T^2test
Hotelling's T^2test for the mean of a multivariate normal distribution ...
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Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard dvariate normal distribution as the unique solution of an initial value problem of a partial differential equation motivated by the harmonic oscillator, which is a special case of a Schrödinger operator. We derive the asymptotic distribution of the test statistics under the hypothesis of normality as well as under fixed and contiguous alternatives. The tests are consistent against general alternatives, exhibit strong power performance for finite samples, and they are applied to a classical data set due to R.A. Fisher. The results can also be used for a neighborhoodofmodel validation procedure.
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