| EHS {mnt} | R Documentation |
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. (2020) "Testing normality in any dimension by Fourier methods in a multivariate Stein equation" arXiv:2007.02596