# Small Area Quantile Estimation

## TL;DR

This paper introduces novel small area quantile estimators using a semiparametric density ratio model, improving accuracy in skewed distributions and providing a resampling method for error estimation.

## Contribution

It develops a new semiparametric density ratio model for small area quantile estimation, enhancing performance over traditional methods especially with skewed data.

## Key findings

- Superior performance with skewed population distributions
- Competitive results with normal distributions
- Resampling procedure effectively estimates mean square errors

## Abstract

Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio-demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives, and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit-level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.