On the smoothness of conditional expectation functionals
Given a class Λ of real functions and a twice differentiable real-valued map φ on R, let Γ be an R-valued functional on Λ of form Γ:λ↦E[Z⋅φ(E[Y∣λ(X)])], where Z and Y are random variables and X is a random vector. This paper calls Γ a conditional expectation functional. Conditional expectation functionals often arise in semiparametric models. The main contribution of this paper is that it provides nontrivial conditions under which Γ has a uniform modulus of continuity with order 2. Hence under these conditions, the functional Γ becomes very smooth.
Volume (Year): 82 (2012)
Issue (Month): 5 ()
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