Effects of model misspecification on small area estimators

TL;DR

This paper investigates how misspecification of mean structures affects small area estimators, revealing that the observed best prediction (OBP) can perform poorly with unit-level auxiliary variables but improves with area-level information.

Contribution

The study provides a Monte Carlo simulation analysis showing the impact of mean structure misspecification on small area estimators and highlights conditions under which OBP performs better.

Findings

OBP may perform poorly with unit-level auxiliary variables.

Using population means of auxiliary variables improves OBP performance.

MSPE of OBP increases with the difference between sample and population means.

Abstract

Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the mean square prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP). Observed Best Prediction (OBP) method has been proposed with the intent to improve on the MSPE over EBLUP. We conduct a Monte Carlo simulation experiment to understand the effect of mispsecification of mean structures on different small area estimators. Our simulation results lead to an unexpected result that OBP may perform very poorly when observational unit level auxiliary variables are used and that OBP can be improved significantly when population means of those auxiliary variables (area level auxiliary variables) are used in the nested error regression model or when a corresponding area level model is used. Our simulation also indicates that the MSPE of OBP in an increasing function of the difference between the sample and population means of the auxiliary variables.