A Q–Q plot for detecting non-multinormality based on a normal characterization and the S–W statistic

Qiang Zhao and Jiajuan Liang

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 5, 1367-1378

Abstract: A quantile-quantile (Q–Q) plot is derived from a characterization for the multivariate normal distribution and the Shapiro–Wilk’s (1965) S–W statistic. The normal characterization results in some independent spherical distributions. The affine invariance of the S–W statistic and a simple property of spherical distributions are employed to construct the Q–Q plot. Easy simulation of the empirical distribution of the S–W statistic avoids the complicated exact null distribution of S-W statistic. The Q–Q plot can be easily implemented for detecting a possible departure from multivariate normality in high dimensional data analysis. Two examples are illustrated for real application.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:51:y:2022:i:5:p:1367-1378

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DOI: 10.1080/03610926.2020.1761983

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