Estimation of a common mean vector in bivariate meta-analysis under the FGM copula |
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| Authors: | Jia-Han Shih Yoshihiko Konno Yuan-Tsung Chang |
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| Affiliation: | 1. Graduate Institute of Statistics, National Central University, Taoyuan, Taiwan;2. Department of Mathematical and Physical Sciences, Japan Women’s University, Tokyo, Japan;3. Department of Social Information, Faculty of Studies on Contemporary Society, Mejiro University, Tokyo, Japan |
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| 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. |
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| Keywords: | Asymptotic theory copula Fisher information maximum likelihood estimation multivariate analysis Stein's identity |
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