Computes the test statistic of the EHS test based on a multivariate Stein equation.
EHS(data, a = 1)a (d,n) numeric matrix containing the data.
positive numeric number (tuning parameter).
The value of the test statistic.
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
$$T_{n,0}=\frac{d}{2}-2^{\frac{d}{2}+1}\frac{1}{n}\sum_{j=1}^n\|Y_{n,j}\|^2\exp(-\frac{\|Y_{n,j}\|^2}{2}).$$
Ebner, B., Henze, N., Strieder, D. (2020) "Testing normality in any dimension by Fourier methods in a multivariate Stein equation" arXiv:2007.02596