test.MKurt {mnt} | R Documentation |
Computes the multivariate normality test based on the classical invariant measure of multivariate sample kurtosis due to Mardia (1970).
test.MKurt(data, MC.rep = 10000, alpha = 0.05)
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 |
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.
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.
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.
test.MKurt(MASS::mvrnorm(50,c(0,1),diag(1,2)),MC.rep=500)