mnt (version 1.3)

test.MKurt: Test of normality based on Mardias measure of multivariate sample kurtosis

Description

Computes the multivariate normality test based on the classical invariant measure of multivariate sample kurtosis due to Mardia (1970).

Usage

test.MKurt(data, MC.rep = 10000, alpha = 0.05)

Arguments

data

a n x d matrix of d dimensional data vectors.

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.

$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

Multivariate sample kurtosis due to Mardia (1970) is defined by $$b_{n,d}^{(2)}=\frac{1}{n}\sum_{j=1}^n\|Y_{n,j}\|^4,$$ where \(Y_{n,j}=S_n^{-1/2}(X_j-\overline{X}_n)\), \(\overline{X}_n\) is the sample mean and \(S_n\) is the sample covariance matrix of the random vectors \(X_1,\ldots,X_n\).To ensure that the computation works properly \(n \ge d+1\) is needed. If that is not the case the test returns an error.

References

Mardia, K.V. (1970), Measures of multivariate skewness and kurtosis with applications, Biometrika, 57:519-530.

Henze, N. (2002), Invariant tests for multivariate normality: a critical review, Statistical Papers, 43:467-506.

See Also

MKurt

Examples

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

# }