*! version 1.2.0 11feb2021
help ellipticity (Vincenzo Verardi and Catherine Vermandele)

Title

ellipticity -- "Optimal" rank-based multivariate tests of elliptical symmetry and sphericity

Syntax

ellipticity varname [if] [in] , [sphericity robust level(#)]

Description

ellipticity performs a multivariate elliptical symmetry test using a semiparametrically efficient optimal
(under gaussianity) rank-based procedure as proposed by Cassart (2007).

When testing for multivariate normality, please see [R] mvtest.

Options

Main

sphericity Specifies that a sphericity test using a semiparametrically efficient
optimal (under gaussianity) rank-based procedure as proposed by Hallin and Paindaveine (2006)
is used instead of the default ellipticity test.

robust Specifies that an S-estimator of location and scatter is used
(instead of the sample mean and covariance matrix) as estimator of the location
and scatter parameters. This makes the tests resistant to outlier contamination.
See Verardi and Croux (2009).

level(#) Specifies the confidence level for confidence intervals. The default
is level(0.95) or as set by set level.

Examples

Setup

webuse auto

Testing for sphericity

ellipticity price mpg headroom weight, sphericity

Testing for ellipticity

ellipticity price mpg headroom weight

same as above but robust to outliers

ellipticity price mpg headroom weight, robust

Saved results

ellipticity saves the following in r():

Scalars

r(Q) The test statistic

r(crit) The critical value

r(df) The degrees of freedom

r(p) The p-value

r(N) The number of observations

e(.) All the outputs available from "robmv s" with the option whilferty called

References

Cassart, D. (2007). Optimal Tests for Symmetry. PhD dissertation,Université Libre de Bruxelles.

Hallin, M. and Paindaveine D. (2006). Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for
sphericity. Annals of Statistics 34, 2707-2756.

Verardi, V. and Croux, C. (2009). Robust regression in Stata. Stata Journal 9(3), 439-453.

Remark

Please type "ssc install robmv" to install robmv, module needed for robust multivariate estimation
of location and scatter. Note that moremata is needed to run robmv. To install it, please type "ssc install moremata"

Also see

Online: help for robmv (if installed)