Robust Small Area Estimation Using Penalized Spline Mixed Models

Small area estimation has been extensively studied under linear mixed models. In particular, empirical best linear unbiased prediction (EBLUP) estimators of small area means and associated estimators of mean squared prediction error (MSPE) that are nearly unbiased have been developed. However, EBLUP estimators can be sensitive to outliers. Sinha and Rao (2009) developed a robust EBLUP method and demonstrated its advantages over the EBLUP under a unit level linear mixed model in the presence of outliers in the random small area effects and/or unit level errors. A bootstrap method of estimating MSPE of the robust EBLUP estimator was also proposed. In this paper, we relax the assumption of linear regression for the fixed part of the model and replace it by a weaker assumption of a penalized spline regression and develop robust EBLUP estimators. Bootstrap estimators of MSPE are also developed. Results of a limited simulation study are summarized.