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The Relationship Between the T2 Statistic and the Influence Function

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  • Robert L. Mason
  • Youn-Min Chou
  • John C. Young

Abstract

Hotelling's T2 statistic has many applications in multivariate analysis. In particular, it can be used to measure the influence that a particular observation vector has on parameter estimation. For example, in the bivariate case, there exists a direct relationship between the ellipse generated using a T2 statistic for individual observations and the hyperbolae generated using Hampel's influence function for the corresponding correlation coefficient. In this paper, we jointly use the components of an orthogonal decomposition of the T2 statistic and some influence functions to identify outliers or influential observations. Since the conditional components in the T2 statistic are related to the possible changes in the correlation between a variable and a group of other variables, we consider the theoretical influence functions of the correlations and multiple correlation coefficients. Finite-sample versions of these influence functions are used to find the estimated influence function values.

Suggested Citation

  • Robert L. Mason & Youn-Min Chou & John C. Young, 2014. "The Relationship Between the T2 Statistic and the Influence Function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2844-2857, July.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:13:p:2844-2857
    DOI: 10.1080/03610926.2012.683129
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