Partial Influence Functions

In this paper we extend the definition of the influence function to functionals of more than one distribution, that is, for estimators depending on more than one sample, such as the pooled variance, the pooled covariance matrix, and the linear discriminant analysis coefficients. In this case the appropriate designation should be “partial influence functions,” following the analogy with derivatives and partial derivatives. Some useful results are derived, such as an asymptotic variance formula. These results are then applied to several estimators of the Mahalanobis distance between two populations and the linear discriminant function coefficients.