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The two-level normal hierarchical model (NHM) has played a critical role inthe theory of small area estimation (SAE), one of the growing areas instatistics with numerous applications in different disciplines. In this paper,we address major well-known shortcomings associated with the empirical bestlinear unbiased prediction (EBLUP) of a small area mean and its mean squarederror (MSE) estimation by considering an appropriate model variance estimatorthat satisfies multiple properties. The proposed model variance estimatorsimultaneously (i) improves on the estimation of the related shrinkage factors,(ii) protects EBLUP from the common overshrinkage problem, (iii) avoids complexbias correction in generating strictly positive second-order unbiased meansquare error (MSE) estimator either by the Taylor series or single parametricbootstrap method. The idea of achieving multiple desirable properties in anEBLUP method through a suitably devised model variance estimator is the firstof its kind and holds promise in providing good inferences for small area meansunder the classical linear mixed model prediction framework. The proposedmethodology is also evaluated using a Monte Carlo simulation study and realdata analysis.

A New Model Variance Estimator for an Area Level Small Area Model to Solve Multiple Problems Simultaneously