Design-based composite estimation of small proportions in small domains

TL;DR

This paper proposes a design-based composite estimation method for small proportions in small domains, combining direct and auxiliary information to improve accuracy over traditional methods.

Contribution

It introduces a robust design-based linear combination estimator and an adaptive procedure optimizing a sample-size-dependent composite estimator for small domain proportions.

Findings

The proposed estimators outperform EBLUP in small domain scenarios.

The methods are effective in estimating employment proportions in Lithuanian municipalities.

The composite estimators provide competitive mean square error estimates.

Abstract

Traditional direct estimation methods are not efficient for domains of a survey population with small sample sizes. To estimate the domain proportions, we combine the direct estimators and the regression-synthetic estimators based on domain-level auxiliary information. For the case of small true proportions, we introduce the design-based linear combination that is a robust alternative to the empirical best linear unbiased predictor (EBLUP) based on the Fay--Herriot model. We also consider an adaptive procedure optimizing a sample-size-dependent composite estimator, which depends on a single parameter for all domains. We imitate the Lithuanian Labor Force Survey, where we estimate the proportions of the unemployed and employed in municipalities. We show where the considered design-based compositions and estimators of their mean square errors are competitive for EBLUP and its accuracy estimation.