Bernoulli

  • Bernoulli
  • Volume 20, Number 4 (2014), 1979-1998.

Restricted likelihood representation and decision-theoretic aspects of meta-analysis

Andrew L. Rukhin

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Abstract

In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. This representation relates the mean effect and the heterogeneity variance estimation problems. An explicit form of the variance of weighted means statistics determined by means of a quadratic form is found. The behavior of the mean squared error for large heterogeneity variance is elucidated. It is noted that the sample mean is not admissible nor minimax under a natural risk function for the number of studies exceeding three.

Article information

Source
Bernoulli, Volume 20, Number 4 (2014), 1979-1998.

Dates
First available in Project Euclid: 19 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1411134450

Digital Object Identifier
doi:10.3150/13-BEJ547

Mathematical Reviews number (MathSciNet)
MR3263095

Zentralblatt MATH identifier
06368423

Keywords
DerSimonian–Laird estimator Hedges estimator Mandel–Paule procedure minimaxity quadratic forms random-effects model Stein phenomenon

Citation

Rukhin, Andrew L. Restricted likelihood representation and decision-theoretic aspects of meta-analysis. Bernoulli 20 (2014), no. 4, 1979--1998. doi:10.3150/13-BEJ547. https://projecteuclid.org/euclid.bj/1411134450


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References

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Supplemental materials

  • Supplementary material: Restricted likelihood representation and decision-theoretic aspects of meta-analysis: Electronic supplement. The supplement contains the proof of Theorem 2.1.