Robust estimation of mean squared error matrix of small area estimators in a multivariate Fay–Herriot model

Abstract

This paper is concerned with the small area estimation in the multivariate Fay–Herriot model where covariance matrix of random effects are fully unknown without normality assumption. The covariance matrix is estimated by a Prasad–Rao type consistent estimator, and the empirical best linear unbiased predictor (EBLUP) of a vector of small area characteristics is provided. When the EBLUP is measured in terms of a mean squared error matrix (MSEM), a second-order approximation of MSEM of the EBLUP and a second-order unbiased estimator of the MSEM are derived analytically in closed forms. The performance is investigated through simulation and empirical studies.