Semi-empirical likelihood confidence intervals for the differences of quantiles with missing data

Detecting population (group) differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed.