Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces

@article{Drr2020TestingMN,
  title={Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces},
  author={Philip D{\"o}rr and Bruno Ebner and Norbert Henze},
  journal={Scandinavian Journal of Statistics},
  year={2020},
  volume={48},
  pages={456 - 501}
}
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… 
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