Empirical likelihood calibration estimation for the median treatment difference in observational studies

The estimation of average (or mean) treatment effects is one of the most popular methods in the statistical literature. If one can have observations directly from treatment and control groups, then the simple t-statistic can be used if the underlying distributions are close to normal distributions. On the other hand, if the underlying distributions are skewed, then the median difference or the Wilcoxon statistic is preferable. In observational studies, however, each individual's choice of treatment is not completely at random. It may depend on the baseline covariates. In order to find an unbiased estimation, one has to adjust the choice probability function or the propensity score function. In this paper, we study the median treatment effect. The empirical likelihood method is used to calibrate baseline covariate information effectively. An economic dataset is used for illustration.