Adjusted maximum likelihood method for multivariate Fay–Herriot model

Abstract

For the Fay–Herriot model, the empirical best linear unbiased predictor (EBLUP) is the weighted sum of direct estimate and regression-synthetic estimate, where the weight depends on the estimate of variance component of random area effects. However, in some cases, the weight of direct survey estimator is zero and the EBLUP reduces to regression-synthetic estimator. This leads to unfavourable estimates. Therefore, Lahiri and Li (2009) introduced the concept of adjusted maximum likelihood method for linear mixed models. The method was then generalized in Li and Lahiri (2010) and Yoshimori and Lahiri (2014) to develop adjusted maximum likelihood consistent variance estimators with positive variance estimates. These adjustments prevent zero weight of direct estimate. In this paper, we extend their methods to propose adjusted maximum likelihood estimates for multivariate Fay–Herriot models. Moreover, we derive their asymptotic properties and perform numerical results to investigate performances of the proposed estimates.