In this paper, a penalized weighted least squares approach is proposed for small area estimation under the unit level model. The new method not only unifies the traditional empirical best linear unbiased prediction that does not take sampling design into account and the pseudo-empirical best linear unbiased prediction that incorporates sampling weights but also has the desirable robustness property to model misspecification compared with existing methods. The empirical small area estimator is given, and the corresponding second-order approximation to mean squared error estimator is derived. Numerical comparisons based on synthetic and real data sets show superior performance of the proposed method to currently available estimators in the literature.
Scopus Subject Areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- basic unit level model
- inverse probability weighted estimation
- penalized least squares
- small area estimation