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Differentiability of the Conditional Expectation

Author

Listed:
  • Hisatoshi Tanaka

    (School of Political Science and Economics, Waseda University)

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.

Suggested Citation

  • Hisatoshi Tanaka, 2020. "Differentiability of the Conditional Expectation," Working Papers 1920, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1920
    as

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    References listed on IDEAS

    as
    1. Song, Kyungchul, 2012. "On the smoothness of conditional expectation functionals," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1028-1034.
    2. Chen, Songnian & Lee, Lung-Fei, 1998. "Efficient Semiparametric Scoring Estimation Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 14(4), pages 423-462, August.
    3. Chen, Songnian, 2000. "Efficient estimation of binary choice models under symmetry," Journal of Econometrics, Elsevier, vol. 96(1), pages 183-199, May.
    4. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
    5. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    6. Crimaldi, Irene, 2004. "On the behavior of the conditional expectations in skorohod representation theorem," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 141-148, April.
    7. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    8. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Binary Response Model; Continuity of Conditional Expectations; Semiparametric Efficiency Bound; Semiparametric Estimation; Single Index Model;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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