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

ABSTRACT

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.

KEYWORDS:

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

Acknowledgements

The authors thank Editor, Associate Editor, and two anonymous reviewers for their detailed and insightful comments and suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was presented in the Japanese Joint Statistical Meeting 2018, Tokyo, Japan. Our work is supported by the government of Taiwan (MOST 105-2118-M-008-001-MY2; 107-2118-M-008-003-MY3) (Ministry of Science and Technology, Taiwan).