Kolmogorov-Smirnov test for matrix normality {MN}

Kolmogorov-Smirnov test for matrix normality

Description

Kolmogorov-Smirnov test for matrix normality

Usage

ddkstest(X, M, U, V, alpha = 0.05)

Arguments

X

A list with k elements, k matrices of dimension n \ times p each. In the case of one matrix only, this may be given as a numerical matrix and not as an element in a list.

M

The mean matrix of the distribution, a numerical matrix of dimensions n \times p.

U

The covariance matrix associated with the rows, a numerical matrix of dimensions n \times n.

V

The covariance matrix associated with the columns, a numerical matrix of dimensions p \times p.

alpha

The significance level for the test, set by default equal to 0.05.

Details

The Kolmogorov-Smirnov test for matrix normality is performed. See Pocuca (2019) for more details.

Value

A message. If the Kronecker product covariance structure is not present, the message reads "Reject" and "Not reject otherwise".

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Pocuca N., Gallaugher M. P., Clark K. M. & McNicholas P. D. (2019). Assessing and Visualizing Matrix Variate Normality. arXiv:1910.02859.

See Also

rmn, mn.mle, dmn, ddplot

Examples

M <- as.matrix(iris[1:8, 1:4])
U <- cov( matrix( rnorm(100 * 8), ncol = 8 ) )
V <- cov( iris[1:50, 1:4] )
X <- rmn(200, M, U, V)
ddkstest(X, M, U, V)