test.MSkew {mnt}

Test of normality based on Mardias measure of multivariate sample skewness

Description

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

Usage

test.MSkew(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

Details

Multivariate sample skewness due to Mardia (1970) is defined by

b_{n,d}^{(1)}=\frac{1}{n^2}\sum_{j,k=1}^n(Y_{n,j}^\top Y_{n,k})^3,

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. Note that for d=1, we have a measure proportional to the squared sample skewness.

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.

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

MSkew

Examples

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