Adjustment of maximum likelihood method for multivariate fay-herriot model

Abstract

The most widely used area-level model in small area estimation is the Fay-Herriot model, proposed by Fay and Herriot. It was used first to estimate average per capita income for small places (population less than 1,000) of the USA. In the context of the Fay-Herriot model, the traditional method in obtaining estimation of the population mean is the empirical best linear unbiased prediction (EBLUP) estimator. The estimate can be expressed as a weighted sum of the direct survey estimator and regression estimator. One problem that has received attention is the estimation of variance of the area random effects in the weight of EBLUP. However, in some cases, the weight of the direct survey estimator is zero and the EBLUP reduces to regression estimator, which is undesirable estimates because it ignores the sample from survey data. Later on, Li and Lahiri proposed adjusted maximum likelihood consistent variance estimators with positive estimates. These adjustments prevent zero weight of the direct estimator. In this study, we extend their methods to adjust the adjusted maximum likelihood method for the multivariate Fay-Herriot model.