test.MAKurt {mnt} | R Documentation |
Computes the multivariate normality test based on the invariant measure of multivariate sample kurtosis due to Malkovich and Afifi (1973).
test.MAKurt(data, MC.rep = 10000, alpha = 0.05, num.points = 1000)
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 |
num.points |
number of points distributed uniformly over the sphere for approximation of the maximum on the sphere. |
Multivariate sample skewness due to Malkovich and Afifi (1973) is defined by
b_{n,d,M}^{(1)}=\max_{u\in \{x\in\mathbf{R}^d:\|x\|=1\}}\frac{\left(\frac{1}{n}\sum_{j=1}^n(u^\top X_j-u^\top \overline{X}_n )^3\right)^2}{(u^\top S_n u)^3},
where \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.
$param
number of points used in approximation.
$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.
Malkovich, J.F., and Afifi, A.A. (1973), On tests for multivariate normality, J. Amer. Statist. Ass., 68:176-179.
Henze, N. (2002), Invariant tests for multivariate normality: a critical review, Statistical Papers, 43:467-506.
test.MAKurt(MASS::mvrnorm(10,c(0,1),diag(1,2)),MC.rep=100)