Empirical Best Linear Unbiased Predictors in Multivariate Nested-Error Regression Models

TL;DR

This paper develops empirical best linear unbiased predictors for multivariate nested-error regression models, providing second-order approximations of mean squared error and confidence intervals for small area estimation.

Contribution

It introduces second-order unbiased estimators for variance components and derives closed-form expressions for MSE and confidence intervals in multivariate nested models.

Findings

Derived second-order unbiased estimators for variance components

Closed-form expressions for MSE and its estimator

Analytical confidence intervals with second-order accuracy

Abstract

For analyzing unit-level multivariate data in small area estimation, we consider the multivariate nested error regression model (MNER) and provide the empirical best linear unbiased predictor (EBLUP) of a small area characteristic based on second-order unbiased and consistent estimators of the `within' and `between' multivariate components of variance. The second-order approximation of the mean squared error (MSE) matrix of the EBLUP and its unbiased estimator are derived in closed forms. The confidence interval with second-order accuracy is also provided analytically.