A Corrected Confidence Interval 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 smallarea 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, theproblem of constructing confidence intervals (cis) when the estimated variance of therandom effect as well as the estimated mean squared error (mse) is negative. moreprecisely, the coverage accuracy of the proposed ci is of the order o(m^-3=2), where m isthe number of sampled areas. the performance of the proposed method is illustratedwith respect to coverage probability (cp) and average length (al) using a simulationexperiment. simulation results demonstrate the superiority of the proposed methodover existing naive cis. in addition, the proposed ci based on the weighted estimatoris comparable with the existing corrected cis based on empirical best linear unbiased predictor (eblup) in the literature.