My reference wasn't correct. The actual reference is: Bickel, Klaassen, Ritov, Wellner, (1998). Efficient and Adaptive Estimation for Semi Parametric Models. Chicago Journal of Theoretical Computer Science. As a note, I don't think this book (or other resources for that matter) offer a truly rigorous construction of the statistical model as a Hilbert manifold. But, if you are familiar with the standard manifold construction, then it should be doable to fill in the details.