Confidence interval estimation of small area parameters shrinking both means and variances

Abstract

We propose a new approach to small area estimation based on joint modelling of means and variances. The proposed model and methodology not only improve small area estimators but also yield “smoothed” estimators of the true sampling variances. Maximum likelihood estimation of model parameters is carried out using EM algorithm due to the non-standard form of the likelihood function. Confidence intervals of small area parameters are derived using a more general decision theory approach, unlike the traditional way based on minimizing the squared error loss. Numerical properties of the proposed method are investigated via simulation studies and compared with other competitive methods in the literature. Theoretical justification for the effective performance of the resulting estimators and confidence intervals is also provided.