MRSSkew {mnt} | R Documentation |
This function computes the invariant measure of multivariate sample skewness due to Móri, Rohatgi and Székely (1993).
MRSSkew(data)
data |
a n x d matrix of d dimensional data vectors. |
Multivariate sample skewness due to Móri, Rohatgi and Székely (1993) is defined by
\widetilde{b}_{n,d}^{(1)}=\frac{1}{n}\sum_{j=1}^n\|Y_{n,j}\|^2\|Y_{n,k}\|^2Y_{n,j}^\top Y_{n,k},
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 function returns an error. Note that for d=1
, it is equivalent to skewness in the sense of Mardia.
value of sample skewness in the sense of Móri, Rohatgi and Székely.
Móri, T. F., Rohatgi, V. K., Székely, G. J. (1993), On multivariate skewness and kurtosis, Theory of Probability and its Applications, 38:547–551.
Henze, N. (2002), Invariant tests for multivariate normality: a critical review, Statistical Papers, 43:467–506.