The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Firework plot for evaluating the impact of outliers in statistical inference

통계적 추론에서 특이점의 영향을 평가하기 위한 탐색적 자료분석 그림도구로서의 불꽃그림

  • Moon, Sungho (Department of Data Management, Busan University of Foreign Studies)
  • 문승호 (부산외국어대학교 데이터경영학과)
  • Received : 2018.02.05
  • Accepted : 2018.02.08
  • Published : 2018.02.28
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Abstract

Outliers and influential observations often distort many numerical measures for data analysis. Jang and Anderson-Cook (Quality and Reliability Engineering International, 30, 1409-1425, 2014) proposed a graphical firework plot method for exploratory analysis purpose to provide a possible visualization of the trace of the impact of the possible outlying and influential observations on the univariate/bivariate data analysis and regression. They developed 3-D plot as well as pairwise plot for the appropriate measures of interest. We use firework plots as a graphical exploratory data analysis tool to detect outliers and evaluate the impact of outliers in statistical inference.

특이점 및 영향점은 자료분석을 하는 데 사용되는 수치적 측도들을 왜곡한다. 각종 자료분석에 있어서의 특이점 검색을 위한 검정 통계량이나 그림도구에 관한 연구는 꾸준히 전개되어 왔다. Jang과 Anderson-Cook (Quality and Reliability Engineering International, 30, 1409-1425, 2014)은 불꽃그림이란 이름을 붙인 그림도구를 발표하였는데 특이점이나 영향점이 일변량/이변량 자료분석 및 회귀분석에 어떠한 영향을 미치는지 알기 위하여 3-D 불꽃그림 및 불꽃그림 행렬을 제시하였다. 본 연구에서는 이러한 불꽃그림이 통계적 추론에서 특이점을 찾아내고 이러한 특이점의 영향을 평가하기 위한 탐색적 자료분석 그림도구로서 사용될 수 있음을 보였다.

Keywords

References

  1. Chatterjee, S. and Hadi, A. S. (2012). Regression Analysis by Example (5th ed), Wiley, Hoboken.
  2. Cook, R. D. (1986). Assessment of local in uence, Journal of Royal Statistical Society, Series B, 48, 133-169.
  3. Fox, J. (2008). Applied Regression Analysis and Generalized Linear Models (2nd ed), Sage, New York.
  4. Hampel, F. R. (1974). The in uence curve and its role in robustness, The Annals of Statistics, 45, 383-393.
  5. Jang, D. H. and Anderson-Cook C. M. (2014). Firework plot as a graphical exploratory data analysis tool for evaluating the impact of outliers in data exploration and regression, Quality and Reliability Engineering International, 30, 1409-1425. https://doi.org/10.1002/qre.1563
  6. Jang, D. H. and Anderson-Cook C. M. (2015). Firework plots for evaluating the impact of outliers and in uential observations in generalized linear models, Quality Technology & Quantitative Management, 12, 419-432.
  7. Jang, D. H. and Anderson-Cook, C. M. (2017). Firework plots for evaluating the impact of outliers and in uential observations in ridge regression, Quality and Reliability Engineering International, 33, 709-725. https://doi.org/10.1002/qre.2050
  8. Maronna, R. A., Martin, D., and Yohai, V. J. (2006). Robust Statistics, John Wiley & Sons, New York.
  9. Montgomery, D. C. (2012). Design and Analysis of Experiments (8th ed), John Wiley & Sons, New York.
  10. Moon, S. (2016). Firework plots for evaluating the impact of outliers and in uential observations in ridge regression, The Korean Journal of Applied Statistics, 29, 355-368. https://doi.org/10.5351/KJAS.2016.29.2.355