test.BHEP {mnt} | R Documentation |
Baringhaus-Henze-Epps-Pulley (BHEP) test
Description
Performs the BHEP test of multivariate normality as suggested in Henze and Wagner (1997) using a tuning parameter a
.
Usage
test.BHEP(data, a = 1, MC.rep = 10000, alpha = 0.05)
Arguments
data |
a n x d matrix of d dimensional data vectors. |
a |
positive numeric number (tuning parameter). |
MC.rep |
number of repetitions for the Monte Carlo simulation of the critical value |
alpha |
level of significance of the test |
Details
The test statistic is
BHEP_{n,\beta}=\frac{1}{n} \sum_{j,k=1}^n \exp\left(-\frac{\beta^2\|Y_{n,j}-Y_{n,k}\|^2}{2}\right)- \frac{2}{(1+\beta^2)^{d/2}} \sum_{j=1}^n \exp\left(- \frac{\beta^2\|Y_{n,j}\|^2}{2(1+\beta^2)} \right) + \frac{n}{(1+2\beta^2)^{d/2}}.
Here, Y_{n,j}=S_n^{-1/2}(X_j-\overline{X}_n)
, j=1,\ldots,n
, are the scaled residuals, \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 test returns an error.
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
Henze, N., Wagner, T. (1997), A new approach to the class of BHEP tests for multivariate normality, J. Multiv. Anal., 62:1-23, DOI
See Also
Examples
test.BHEP(MASS::mvrnorm(50,c(0,1),diag(1,2)),MC.rep=500)