Relationships Between the T-Square Statistic and the Influence Function

• Activity Number: 254
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Robert L. Mason*+ and Youn-Min Chou and John C. Young
• Companies: Southwest Research Institute and The University of Texas at San Antonio and Retired
• Keywords: correlation coefficient ; influential observation ; MYT decomposition

Abstract

Hotelling's T-Square 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 T-Square statistic for a single observation and the hyperbola generated using Hampel's influence function for the corresponding correlation coefficient. In this paper, we jointly use the components of the T-Square statistic in the MYT decomposition and some influence functions to identify outliers or influential observations. Since the conditional components in the T-Square statistics are related to the possible changes in the correlation between a variable and a group of other variables, we consider the true influence functions of the correlations and multiple correlation coefficients. Two finite-sample versions of the true influence functions are used to find the estimated influence function values.