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Characterization-based Q-Q plots for testing multinormality

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  • Liang, Jiajuan
  • Pan, William S.Y.
  • Yang, Zhen-Hai

Abstract

Three quantile-quantile (Q-Q) plots are derived from a characterization for the multivariate normal distribution. The Q-Q plots can be easily used for detecting a possible departure from multinormality in high-dimensional data analysis. An example is illustrated to employ the plots in practice.

Suggested Citation

  • Liang, Jiajuan & Pan, William S.Y. & Yang, Zhen-Hai, 2004. "Characterization-based Q-Q plots for testing multinormality," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 183-190, December.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:183-190
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    References listed on IDEAS

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    1. J. P. Royston, 1983. "Some Techniques for Assessing Multivarate Normality Based on the Shapiro‐Wilk W," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 121-133, June.
    2. Fang, Kai-Tai & Li, Run-Ze & Liang, Jia-Juan, 1998. "A multivariate version of Ghosh's T3-plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 371-386, October.
    3. M. J. R. Healy, 1968. "Multivariate Normal Plotting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 17(2), pages 157-161, June.
    4. Yang, Zhen-Hai & Fang, Kai-Tai & Liang, Jia-Juan, 1996. "A characterization of multivariate normal distribution and its application," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 347-352, November.
    5. Liang, Jia-Juan & Bentler, Peter M., 1999. "A t-distribution plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 31-44, March.
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    1. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    2. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    3. Jacqueline Karlsson & Helena Melin & Kevin Cullinane, 2018. "The impact of potential Brexit scenarios on German car exports to the UK: an application of the gravity model," Journal of Shipping and Trade, Springer, vol. 3(1), pages 1-22, December.

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