Empirical best prediction of small area bivariate parameters

TL;DR

This paper develops empirical best predictors for small area bivariate parameters using a bivariate nested error regression model, with MSE estimation via bootstrap, validated through simulations and applied to Spanish household expenditure data.

Contribution

It introduces a novel empirical best prediction method for bivariate small area parameters under a nested error model, with MSE estimation and practical application.

Findings

Method performs well in simulations.

Provides accurate estimators for real data.

Demonstrates applicability to household expenditure data.

Abstract

This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit-level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces.