On Rotational Robustness of Shapiro-Wilk Type Tests for Multivariate Normality

Richie Lee, Meng Qian, Yongzhao Shao

Division of Biostatistics, New York University School of Medicine, New York, USA.

DOI: 10.4236/ojs.2014.411090                

Abstract

The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality; thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.

Keywords

Multivariate Normality, R Packages, Robust Power, Shapiro-Wilk Test, Rotational Robustness

Conflicts of Interest

The authors declare no conflicts of interest.

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