Description Usage Arguments Value Background References Examples
Test for elliptical symmetry based on the averages of spherical harmonics.
1  MPQ(X, epsilon = 0.05)

X 
A numeric matrix. 
epsilon 
A value which indicates the proportion of points close to the origin which will not be used in the calculation. Default is set to 0.05. 
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. 
Test for elliptical symmetry based on spherical harmonics of degrees 3 and 4. The test statistic involves the averages of spherical harmonics over the projections of the scale residuals on the unit sphere. This test requires moments of order 4, it has a simple asymptotic distribution but does not have asymptotic power 100% against all alternatives.
Manzotti, A., Perez, Francisco J., & Quiroz, Adolfo J. (2002). A statistic for testing the null hypothesis of elliptical symmetry. Journal of Multivariate Analysis, 81(2), 274285.
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