Empirical influence function (${\mathrm{EIF}}_n(z)=\mathrm{IF}(z;T,F_n)$)

This plugs the empirical distribution into the population influence function. For an M-estimator it is $-[n^{-1}{\sum }_i{\partial }_{\theta }\psi (y_i,T(F_n)){]}^{-1}\psi (z,T(F_n))$, when this denominator is well-defined and nonzero. For functionals involving a density at a quantile, an unsmoothed empirical measure may not permit this derivative, so smoothing or an actual sensitivity curve is required.