test.CS {mnt} | R Documentation |
multivariate normality test of Cox and Small
Description
Performs the test of multivariate normality of Cox and Small (1978).
Usage
test.CS(data, MC.rep = 1000, alpha = 0.05, Points = NULL)
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. |
Points |
number of points to approximate the maximum functional on the unit sphere. |
Details
The test statistic is ,
where
.
Here, ,
, are the scaled residuals,
is the sample mean and
is the sample covariance matrix of the random vectors
. To ensure that the computation works properly
is needed. If that is not the case the test returns an error. Note that the maximum functional has to be approximated by a discrete version, for details see Ebner (2012).
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
Cox, D.R., Small, N.J.H. (1978), Testing multivariate normality, Biometrika, 65:263-272.
Ebner, B. (2012), Asymptotic theory for the test for multivariate normality by Cox and Small, Journal of Multivariate Analysis, 111:368-379.
See Also
Examples
test.CS(MASS::mvrnorm(10,c(0,1),diag(1,2)),MC.rep=100)