Small Area Quantile Estimation

Abstract

Summary 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.

A bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data, with applications to analysis of quality of life outcomes in clinical trials

“…The DRM is also closely connected with several classical statistical models, such as parametric exponential family, logistic regression and biased sampling . The DRM has been found successful in various multisample inference problems . In the next section, we apply the empirical likelihood method to develop a semiparametric test for H 0 under the above models and .…”

Beta-Binomial Model in Small Area Estimation Using Hierarchical Likelihood Approach

“…The application of this study was carried out on remote sensing data. A small area quantitative estimator with a semiparametric density ratio model for the error distribution at the unit level nested error regression model has been developed by Chen & Liu (2019). Salvati et al (2021) developed a small area estimation model on the data linkage.…”

Empirical likelihood ratio test on quantiles under a density ratio model

“…In forestry, the lower quantiles of the mechanical strength of wood products are vital design values (Verrill et al, 2015). Other examples include Chen and Hall (1993); Yang and He (2012); Chen and Liu (2013); Chen et al (2016); Koenker et al (2017); Gonçalves et al (2020); Chen and Liu (2019).…”