Computes the (approximated) Pudelko test of multivariate normality.
Usage
test.PU(data, MC.rep = 10000, alpha = 0.05, r = 2)
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.
r
a positive number (radius of Ball)
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.
$param
value tuning parameter.
$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.
Details
This functions evaluates the test statistic with the given data and the specified parameter r. Since since one has to calculate the supremum of a function inside a d-dimensional Ball of radius r. In this implementation the optim function is used.
References
Pudelko, J. (2005), On a new affine invariant and consistent test for multivariate normality, Probab. Math. Statist., 25:43-54.