Influence on Hotelling s Test Statistic

A diagnostic method of identifying influential observations in performing the Hotelling s T^2 test based on influence function is suggested by defining an appropriate functional whose value at the empirical distribution functions becomes the Hotelling s T^2 statistic. The maximum likelihood estimators are very sensitive to influential observations so that the Hotelling s T^2 statistic would be vulnerable to influential observations. The diagnostic method based on influence function may be useful for measuring the influence of observations on the Hotelling s T^2 statistic and it can be adapted to other statistical problems. A numerical example is provided for illustration.