**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series B, Pt. 3, pp. 323--337

**FIRST ORDER LOCAL INFLUENCE OF TEST STATISTICS IN MULTIVARIATE REGRESSION**

By

M. K. TANG and WING K. FUNG, *The University of Hong Kong, Hong Kong*

SUMMARY. Four tests statistics, namely, the Wilk's ratio, Lawley-Hotelling trace, Pillai's trace and Roy's maximum root in multivariate regression, instead of the usual likelihood displacement, are used for local influence analysis. The first order local influence approach studies the first derivatives of these test statistics . Three different perturbation schemes such as case-weights, explanatory variables and response variables are adopted for local influence assessment.

*AMS (1991) subject classification.* 62H15, 62J99.

*Key words and phrases.* Diagnostics, local influence, hypothesis testing, multivariate regression, perturbation.