Pseudo Empirical Best Prediction of Multiple Characteristics in Small Areas

TL;DR

This paper develops a multivariate pseudo-empirical best predictor for small area estimation that accounts for complex sampling designs and multiple dependent variables, improving bias correction and estimator accuracy.

Contribution

It introduces a unified multivariate predictor under a nested error model that incorporates sampling design and can be derived from unit or area-level data.

Findings

Proposed predictors show reduced bias in simulations.

Bootstrap methods effectively estimate mean squared errors.

Application demonstrates practical utility in housing data analysis.

Abstract

Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under unit-level models typically focus on a single response variable. This paper addresses the estimation of area means for several dependent target variables under a multivariate nested error regression (MNER) model. We propose a multivariate pseudo-empirical best linear unbiased predictor that accounts for the sampling mechanism. Moreover, by aggregating the MNER model, we derive a unified predictor that can be obtained from either unit-level or area-level data. Bootstrap procedures are proposed to estimate the mean squared errors (MSEs) of the proposed predictors. Simulation experiments are conducted to examine the properties of the proposed small area estimators and the MSE estimators. Finally, an application with housing data illustrates the proposed methods.