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

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.