Empirical likelihood in a semi-parametric model for missing response data

Let Y be a response and, given covariate X , Y has a conditional density f ( y | x , ?), where ? is a unknown p -dimensional vector of parameters and the marginal distribution of X is unknown. When responses are missing at random, with auxiliary information and imputation, we define an adjusted empirical log-likelihood ratio for the mean of Y and obtain its asymptotic distribution. A simulation study is conducted to compare the adjusted empirical log-likelihood and the normal approximation method in terms of coverage accuracies.