Corrected Confidence Intervals for a Small Area Parameter through the Weighted Estimator under the Basic Area Level Model

Area level linear mixed models can be generally applied to produce small area indirect estimators when only aggregated data such as sample means are available. This paper tries to fill an important research gap in small area estimation literature, the problem of constructing confidence intervals (CIs) when the estimated variance of the random effect as well as the estimated mean squared error (MSE) is negative. More precisely, the coverage, accuracy of the proposed CI is of the order O(m−3/2), where m is the number of sampled areas. The performance of the proposed method is illustrated with respect to coverage probability (CP) and average length (AL) using a simulation experiment. Simulation results demonstrate the superiority of the proposed method over existing naive CIs. In addition, the proposed CI based on the weighted estimator is comparable with the existing corrected CIs based on empirical best linear unbiased predictor (EBLUP) in the literature.