PseudoGaussian {ellipticalsymmetry} | R Documentation |
Tests for elliptical symmetry: specified and unspecified location.
PseudoGaussian(X, location = NA)
X |
A numeric matrix. |
location |
A vector of location parameters. |
Note that location
allows the user to specify the known location.
The default is set to NA
which means that the unspecified location test will be performed unless the user specifies location.
An object of class "htest"
containing the following components:
statistic |
The value of the test statistic. |
pvalue |
The p-value of the test. |
alternative |
A character string describing the alternative hypothesis. |
method |
A character string indicating what type of test was performed. |
Pseudo-Gaussian tests for elliptical symmetry are based on Le Camâ€™s theory of statistical experiments. They are most efficient against a multivariate form of Fechner-type asymmetry. These tests require finite moments of order 4 and they have a simple asymptotic chi-squared distribution under the null hypothesis of ellipticity.
Cassart, D., Hallin, M. & Paindaveine, D., (2008). Optimal detection of Fechner-asymmetry. Journal of Statistical Planning and Inference, 138, 2499-2525.
Cassart, D., (2007). Optimal tests for symmetry. Ph.D. thesis, Univ. libre de Bruxelles, Brussels.
## sepal width and length of the versicolor subset of the Iris data
X = datasets::iris[51:100,1:2]
PseudoGaussian(X)