mnt (version 1.3)

test.HV: The Henze-Visagie test of multivariate normality

Description

Computes the multivariate normality test of Henze and Visagie (2019).

Usage

test.HV(data, a = 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.

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.

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.

References

Henze, N., Visagie, J. (2019) "Testing for normality in any dimension based on a partial differential equation involving the moment generating function", to appear in Ann. Inst. Stat. Math., DOI

See Also

HV

Examples

# NOT RUN {
test.HV(MASS::mvrnorm(50,c(0,1),diag(1,2)),a=5,MC.rep=500)
test.HV(MASS::mvrnorm(50,c(0,1),diag(1,2)),a=Inf,MC.rep=500)

# }