ABSTRACT
Definition 2.1 The Gaˆteau derivative of functional T in distribution P in the direction of Dirac distribution δx, x ∈ X is called the influence function of T in P ; thus
IF (x;T, P ) = T ′x(P ) = limt→0+ T (Pt(δx))− T (P )
t (2.2)
where Pt(δx) = (1− t)P + tδx. As the first main properties of IF, let us mention:
a) EP (IF (x;T, P )) = ∫ X T
′ x(P )dP = 0,
hence the average influence of all points x on the estimation error is zero.
