PseudoGaussian: Pseudo-Gaussian test for elliptical symmetry

In ellipticalsymmetry: Elliptical Symmetry Tests

Description

Tests for elliptical symmetry: specified and unspecified location.

Usage

PseudoGaussian(X, location = NA)

Arguments

X	A numeric matrix.
location	A vector of location parameters.

Details

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.

Value

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.

Background

Pseudo-Gaussian tests for elliptical symmetry are based on Le Cam’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.

References

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.

Examples

## sepal width and length of the versicolor subset of the Iris data
X = datasets::iris[51:100,1:2]

PseudoGaussian(X)

ellipticalsymmetry documentation built on April 7, 2021, 5:06 p.m.