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Extension of Stein's Lemmas to General Functions and Distributions

Author

Listed:
  • Moawia Alghalith

    (University of the West Indies)

  • Wing-Keung Wong

    (Department of Finance, Fintech Center, and Big Data Research Center, Asia University)

Abstract

In this paper, we extend the lemmas in Stein (1973, 1981) and others to include situations in which the variables are dependent and non-normally distributed. There is no restriction on the form of the function, which could be linear or nonlinear, provided that the function is differentiable and the expectation of the derivative of the function exists. Thereafter, we give some examples of nonnormal distributions and nonlinear functions to illustrate the theorems developed in the paper to hold, and show that the assertion of Genest (2020) is incorrect. In addition, we discuss applications of using the theorems in decision sciences.

Suggested Citation

  • Moawia Alghalith & Wing-Keung Wong, 2020. "Extension of Stein's Lemmas to General Functions and Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(4), pages 77-88, December.
    • Handle: RePEc:aag:wpaper:v:24:y:2020:i:4:p:77-88
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    References listed on IDEAS

    as
    1. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2015. "Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 889-900, May.
    2. Wong, Wing-keung & Miller, Robert B, 1990. "Repeated Time Series Analysis of ARIMA-Noise Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 243-250, April.
    3. Landsman, Zinoviy & Vanduffel, Steven & Yao, Jing, 2015. "Some Stein-type inequalities for multivariate elliptical distributions and applications," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 54-62.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Stein's Lemma; dependence; non-normality; differentiability; expectations;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • G0 - Financial Economics - - General

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