Open AccessSmall area quantile estimation based on distribution function using linear mixed models
Author(s) -
Tomasz Stachurski
Publication year - 2021
Publication title -
economics and business review/the poznań university of economics review
Language(s) - English
Resource type - Journals
eISSN - 2392-1641
pISSN - 1643-5877
DOI - 10.18559/ebr.2021.2.7
Subject(s) - quantile , estimator , mathematics , quantile function , statistics , function (biology) , distribution (mathematics) , mean squared error , econometrics , mathematical optimization , probability density function , cumulative distribution function , mathematical analysis , evolutionary biology , biology
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.