Small area quantile estimation based on distribution function using linear mixed models

In economic studies researchers are often interested in the estimation of the distribution function or certain functions of the distribution function such as quantiles. This work focuses on the estimation quantiles as inverses of the estimates of the distribution function in the presence of auxiliary information that is correlated with the study variable. In the paper a plug-in estimator of the distribution function is proposed which is used to obtain quantiles in the population and in the small areas. Performance of the proposed method is compared with other estimators of the distribution function and quantiles using the simulation study. The obtained results show that the proposed method usually has smaller relative biases and relative RMSE comparing to other methods of obtaining quantiles based on inverting the distribution function.