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On the smoothness of conditional expectation functionals

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  • Song, Kyungchul
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000375
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 5 ()
    Pages: 1028-1034

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:1028-1034

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    Related research

    Keywords: Conditional expectation functionals; Discretization; Uniform modulus of continuity; Semiparametric models;

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    Cited by:
    1. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    2. Song, Kyungchul, 2014. "Semiparametric models with single-index nuisance parameters," Journal of Econometrics, Elsevier, vol. 178(P3), pages 471-483.

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