EHS: Statistic of the EHS test based on a multivariate Stein...

In mnt: Affine Invariant Tests of Multivariate Normality

Statistic of the EHS test based on a multivariate Stein equation

Description

Computes the test statistic of the EHS test based on a multivariate Stein equation.

Usage

EHS(data, a = 1)

Arguments

data	a (d,n) numeric matrix containing the data.
a	positive numeric number (tuning parameter).

Details

This functions evaluates the teststatistic with the given data and the specified tuning parameter a. Each row of the data Matrix contains one of the n (multivariate) sample with dimension d. To ensure that the computation works properly n \ge d+1 is needed. If that is not the case the test returns an error.

Note that a=Inf returns the limiting test statistic with value 2*MSkew + MRSSkew and a=0 returns the value of the limit statistic

T_{n,0}=\frac{d}{2}-2^{\frac{d}{2}+1}\frac{1}{n}\sum_{j=1}^n\|Y_{n,j}\|^2\exp(-\frac{\|Y_{n,j}\|^2}{2}).

Value

The value of the test statistic.

References

Ebner, B., Henze, N., Strieder, D. (2022) "Testing normality in any dimension by Fourier methods in a multivariate Stein equation", The Canadian Journal of Statistics, 50(3): 992-1033, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/cjs.11670")}.

mnt documentation built on Sept. 25, 2026, 5:08 p.m.