Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

This paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ( $$d\ge 2$$ ), which has $$2^d-d-1$$ dependence parameters to be estimated; therefore, maximum likelihood estimation is not practical for a large d from the viewpoint of computational complexity. Besides, the restriction for the FGM copula’s parameters becomes increasingly complex as d becomes large, which makes parameter estimation difficult. We propose an effective estimation algorithm for the d-variate FGM copula by using the method of inference functions for margins under the restriction of the parameters. We then discuss its asymptotic normality as well as its performance determined through simulation studies. The proposed method is also applied to real data analysis of bearing reliability.