test.PU {mnt}

Pudelko test of multivariate normality

Description

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)

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.

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.

References

Pudelko, J. (2005), On a new affine invariant and consistent test for multivariate normality, Probab. Math. Statist., 25:43-54.

See Also

PU

Examples

test.PU(MASS::mvrnorm(20,c(0,1),diag(1,2)),r=2,MC=100)