Extend the equivalence to non-smooth functionals

Extend the equivalence between Neyman orthogonality and pathwise differentiability to settings in which the parameter of interest or the estimating function is non-smooth (for example, not Fréchet differentiable in L2), and ascertain conditions under which the equivalence continues to hold.

Background

The main results establish the equivalence under smoothness assumptions, including Fréchet differentiability of the estimating function in L2 and differentiability of coordinate paths along regular submodels. These smoothness conditions exclude certain non-smooth parameters common in semiparametric inference.

The authors explicitly list extending the equivalence to non-smooth functionals as an open direction, indicating that broadened theory would cover a wider class of targets encountered in practice.

References

Several directions remain open. Foremost, the regularity conditions we impose, notably the existence of coordinate submodels witnessing local product structure, can be nontrivial to verify in complex semiparametric problems, such as those involving constrained nuisance spaces or functionals defined through implicit equations. Relaxing these conditions, extending the equivalence to settings with non-smooth functionals, and developing systematic tools for constructing coordinate submodels in applied problems would be natural next steps.

— On the Equivalence between Neyman Orthogonality and Pathwise Differentiability  (2603.15817 - Chen et al., 16 Mar 2026) in Section 4 (Discussion)