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Posterior expectation based on empirical likelihoods

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  • A. Vexler
  • G. Tao
  • A. D. Hutson

Abstract

Posterior expectation is widely used as a Bayesian point estimator. In this note we extend it from parametric models to nonparametric models using empirical likelihood, and develop a nonparametric analogue of James–Stein estimation. We use the Laplace method to establish asymptotic approximations to our proposed posterior expectations, and show by simulation that they are often more efficient than the corresponding classical nonparametric procedures, especially when the underlying data are skewed.

Suggested Citation

  • A. Vexler & G. Tao & A. D. Hutson, 2014. "Posterior expectation based on empirical likelihoods," Biometrika, Biometrika Trust, vol. 101(3), pages 711-718.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:711-718.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu018
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    Cited by:

    1. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Albert Vexler & Li Zou & Alan D. Hutson, 2016. "Data-Driven Confidence Interval Estimation Incorporating Prior Information with an Adjustment for Skewed Data," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 243-249, July.
    3. Vexler, Albert & Zou, Li & Hutson, Alan D., 2019. "The empirical likelihood prior applied to bias reduction of general estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 96-106.

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