Empirical Likelihood in Generalized Linear Models with Working Covariance Matrix

Empirical likelihood in generalized linear models with multivariate responses and working covariance matrix is discussed. Under the weakest assumption on eigenvalues of Fisher’s information matrix and some other regular conditions, we prove that the non-parametric Wilk’s property still holds, that is, the empirical log-likelihood ratio at the true parameter values converges to the standard chi-square distribution. Numerical simulations are given to verify our theoretical result.