A UNIFIED MEASURE OF UNCERTAINTY OF ESTIMATED BEST LINEAR UNBIASED PREDICTORS IN SMALL AREA ESTIMATION PROBLEMS

摘要: We obtain a second order approximation to the mean squared error (MSE), and its estimate, of empirical or estimated best linear unbiased pre- dictor (EBLUP) mixed effect in general normal model. This covers many important small area models literature. Unlike previous research this area, we provide unified theory measuring uncertainty an EBLUP for complex model where variance components are by vari- ous standard methods including restricted residual maximum likelihood (REML) (ML). It turns out that MSE approximations REML ML exactly same asymptotic sense. However, accurate estimator based on for- mer method requires less bias correction than one latter method. is due result paper which shows esti- mators lower estimators. A simulation undertaken compare different estimating study properties various estimators effect. In our context it interesting note as conditional profile (CPL) Cox Reid (1987). Thus, addresses open problem raised (1987) prediction using CPL