On the smoothness of conditional expectation functionals

Kyungchul Song

Statistics & Probability Letters, 2012, vol. 82, issue 5, 1028-1034

Abstract: 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.

Keywords: Conditional expectation functionals; Discretization; Uniform modulus of continuity; Semiparametric models (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spl.2012.01.027

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