test.EHS {mnt}

Ebner-Henze-Strieder test of multivariate normality based on Fourier methods in a multivariate Stein equation

Description

Computes the multivariate normality test of Ebner, Henze and Strieder (2020) based on Fourier methods in a multivariate Stein equation.

Usage

test.EHS(data, a = 0.5, MC.rep = 10000, alpha = 0.05)

Arguments

data

a n x d matrix of d dimensional data vectors.

a

positive numeric number (tuning parameter).

MC.rep

number of repetitions for the Monte Carlo simulation of the critical value.

alpha

level of significance of the test.

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.

Value

a list containing the value of the test statistic, the approximated critical value and a test decision on the significance level alpha:

$Test

name of the test.

$param

value tuning parameter.

$Test.value

the value of the test statistic.

$cv

the approximated critical value.

$Decision

the comparison of the critical value and 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

See Also

EHS

Examples

test.EHS(MASS::mvrnorm(50,c(0,1),diag(1,2)),a=1,MC=500)