The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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An Approximate Shapiro -Wilk Statistic for Testing Multivariate Normality

다변량 정규성검정을 위한 근사 SHAPIRO-WILK 통계량의 일반화

  • Published : 2004.03.01
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Abstract

In this paper, we generalizes Kim and Bickel(2003)'s statistic for bivariate normality to that of multinormality, applying Fattorini(1986)'s method. Fattorini(1986) generalized Shapiro-Wilk's statistic for univariate normality to multivariate cases. The proposed statistic could be considered as an approximate statistic to Fattorini(1986)'s. It can be used even for a big sample size. Power performance of the proposed test is assessed in a Monte Carlo study.

본 논문에서는 Kim & Bickel(2003)에서 제안한 이변량 정규분포를 위한 검정통계량을 Fattorini(1986)의 방법을 이용하여 이변량 이상인 경우에도 실제적으로 사용가능 하도록 일반화하였다. Fattorini(1986)의 통계량은 Shapiro & Wilk(1965)의 일변량 정규분포를 위한 검정통계량을 다변량으로 확장한 것이다. 그리고 제안된 통계량은 Fat-torini(1986) 통계량의 근사통계량으로 생각할 수 있으며 표본의 크기가 클 때도 사용 가능하다. 또한 모의실험을 통하여 여러 가지 대립가설에서 기존의 통계량과의 검정력을 비교하였다.

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  1. Multivariate Normality Tests Based on Principal Components vol.10, pp.3, 2003, https://doi.org/10.5351/CKSS.2003.10.3.765
  2. Tests Based on Skewness and Kurtosis for Multivariate Normality vol.22, pp.4, 2015, https://doi.org/10.5351/CSAM.2015.22.4.361