Each week, we select a recently published Open Access article to feature. This week’s article comes the Scandinavian Journal of Statistics and examines affine invariant and consistent tests for normality. The article was published in the latest issue of the journal as part of a special issue based on the 4th Workshop on Goodness‐of‐Fit, Change‐Point and Related Problems, Trento 2019.
The article’s abstract is given below, with the full article available to read here.
More Details Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces
. Scand J Statist
, , .
We study a novel class of affine invariant and consistent tests for normality in any dimension in an i.i.d.-setting. The tests are based on a characterization of the standard d-variate 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 neighborhood-of-model validation procedure.