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MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness

1
Dipartimento di Scienze Agrarie e Forestali (DAFNE), Università degli Studi della Tuscia, Via San Camillo de Lellis snc, 01100 Viterbo, Italy
2
Dipartimento di Economia, Società e Politica (DESP), Università degli Studi di Urbino “Carlo Bo”, Via Saffi 42, 61029 Urbino, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(8), 970; https://doi.org/10.3390/sym11080970
Received: 6 July 2019 / Revised: 17 July 2019 / Accepted: 22 July 2019 / Published: 1 August 2019
(This article belongs to the Special Issue Recent Advances on Symmetry in Mathematical Statistics)
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Abstract

The R packages MaxSkew and MultiSkew measure, test and remove skewness from multivariate data using their third-order standardized moments. Skewness is measured by scalar functions of the third standardized moment matrix. Skewness is tested with either the bootstrap or under normality. Skewness is removed by appropriate linear projections. The packages might be used to recover data features, as for example clusters and outliers. They are also helpful in improving the performances of statistical methods, as for example the Hotelling’s one-sample test. The Iris dataset illustrates the usages of MaxSkew and MultiSkew. View Full-Text
Keywords: asymmetry; bootstrap; projection pursuit; symmetrization; third cumulant asymmetry; bootstrap; projection pursuit; symmetrization; third cumulant
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Franceschini, C.; Loperfido, N. MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness. Symmetry 2019, 11, 970.

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