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ω (0) = 0 such that 

<img src='content_image/315583.jpg'>

Remark 8. A sufficient, but not necessary, condition for such an ω to exist is that F$_{π}$ is twice continuously differentiable with the absolute range of the second derivative ¨ F$_{π}$ on [ V ( π ) ± c ] bounded away from infinity uniformly in π ∈ Π. Indeed, Taylor’s theorem then shows that one can take 

<img src='content_image/315584.jpg'>

The next lemma gives conditions under which (9) holds. Its proof is given in Ap- pendix B.3. 

Lemma 9. If (15) and (16) are met, then (9) holds. 

For every π ∈ P , V ( π ) defined in (14) can be viewed as the evaluation at P of the functional 

from the nonparametric model of distributions P ′ satisfying the same constraints as P to the real line. This functional is pathwise differentiable at P relative to the maximal tangent space with an efficient influence function f$_{π}$ given by 

<img src='content_image/315585.jpg'>

<img src='content_image/315586.jpg'>

Observe that above ˙ F$_{π}$ ( V ( π )) only enters f$_{π}$ as a multiplicative constant, and therefore an estimating equation-based estimator or TMLE for V ( π ) can be asymptotically linear for V ( π ) 

