Estimation of a common mean vector in bivariate meta-analysis under the FGM copula

Jia Han Shih, Yoshihiko Konno, Yuan Tsung Chang, Takeshi Emura*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

14 Scopus citations


We propose a bivariate Farlie–Gumbel–Morgenstern (FGM) copula model for bivariate meta-analysis, and develop a maximum likelihood estimator for the common mean vector. With the aid of novel mathematical identities for the FGM copula, we derive the expression of the Fisher information matrix. We also derive an approximation formula for the Fisher information matrix, which is accurate and easy to compute. Based on the theory of independent but not identically distributed (i.n.i.d.) samples, we examine the asymptotic properties of the estimator. Simulation studies are given to demonstrate the performance of the proposed method, and a real data analysis is provided to illustrate the method.

Original languageEnglish
Pages (from-to)673-695
Number of pages23
Issue number3
StatePublished - 04 05 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Asymptotic theory
  • Fisher information
  • Stein's identity
  • copula
  • maximum likelihood estimation
  • multivariate analysis


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