Description Usage Arguments Details Value Background References Examples
Tests for elliptical symmetry: specified and unspecified location.
1  SkewOptimal(X, location = NA, f = "t", param = NA)

X 
A numeric matrix. 
location 
A vector of location parameters. 
f 
A string that specifies the type of the radial density upon which the test is based. Currently supported options are 
param 
A parameter that is used when 
X
and location
are the only input arguments for the specified location test.
The default value for location
is set to NA
which implies that the unspecified location test will be performed
unless the user specifies location.
For the unspecified location test, besides the data matrix X
, the input arguments are f
and param
.
The f
argument is a string that specifies the type of the radial density upon which the test is based.
Currently supported options are: "t"
for the radial density of the multivariate t distribution,
"logistic"
for the multivariate logistic and "powerExp"
for the radial density of the multivariate powerexponential distribution.
Note that the default is set to "t"
.
The role of the param
argument is as follows.
If f = "t"
then param
denotes the degrees of freedom of the multivariate t distribution.
Given that the default radial density is "t"
, it follows that the default value of param
represents the degrees of freedom of the multivariate t distribution and it is set to 4.
Note also that the degrees of freedom have to be greater than 2.
If f = "powerExp"
then param
denotes the kurtosis parameter. In that case the value of param
has to be different from 1, because for the multivariate power exponential distribution, a kurtosis parameter equal to 1 corresponds
to the multivariate Gaussian distribution (the Gaussian f
is excluded due to a singular Fisher information matrix).
The default value is set to 0.5.
An object of class "htest"
containing the following components:

The value of the test statistic. 

The pvalue of the test. 

A character string describing the alternative hypothesis. 

A character string indicating what type of test was performed. 
Tests for elliptical symmetry both for specified and unspecified location. These tests are based on Le Cam’s theory of statistical experiments and they are optimal against generalized skewelliptical alternatives, but they remain quite powerful under a much broader class of nonelliptical distributions. They have a simple asymptotic chisquared distribution under the null hypothesis of ellipticity, they are affineinvariant, computationally fast, have a simple and intuitive form, only require finite moments of order 2.
Babic, S., Gelbgras, L., Hallin, M., & Ley, C. (2021). Optimal tests for elliptical symmetry: specified and unspecified location. Bernoulli (in press).
1 2 3 4 5 6 7 8 9 10 11 12  ## sepal width and length of the versicolor subset of the Iris data
X = datasets::iris[51:100,1:2]
## location unspecified test based on the radial density of the multivariate t distribution
SkewOptimal(X)
## location unspecified test based on the radial density of the logistic distribution
SkewOptimal(X, f="logistic")
## location unspecified test based the radial density of the power exponential distribution
SkewOptimal(X, f="powerExp")

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