Differentiability of the Conditional Expectation

Hisatoshi Tanaka ()
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Hisatoshi Tanaka: School of Political Science and Economics, Waseda University

No 1920, Working Papers from Waseda University, Faculty of Political Science and Economics

Abstract: The differentiability of a random function b 7→ E(Y |Gb(X)) is presented in this study. The function is shown to be differentiable if Gb(X) is continuously distributed. The result is applied to the semiparametric single-index model E(Y |X) = F(Gβ(X)), and a quick way to compute the efficiency bound for estimating β has been proposed.

Keywords: Binary Response Model; Continuity of Conditional Expectations; Semiparametric Efficiency Bound; Semiparametric Estimation; Single Index Model (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 9 pages
Date: 2020-01
New Economics Papers: this item is included in nep-ore
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