Robust small area estimation under semi‐parametric mixed models

Abstract

AbstractSmall area estimation has been extensively studied under unit level linear mixed models. In particular, empirical best linear unbiased predictors (EBLUPs) of small area means and associated estimators of mean squared prediction error (MSPE) that are unbiased to second order have been developed. However, EBLUP can be sensitive to outliers. Sinha & Rao (2009) developed a robust EBLUP method and demonstrated its advantages over the EBLUP in the presence of outliers in the random small area effects and/or unit level errors in the model. A bootstrap method for estimating MSPE of the robust EBLUP was also proposed. In this paper, we relax the assumption of linear regression for the fixed part of the model and we replace it by a weaker assumption of a semi‐parametric regression. By approximating the semi‐parametric mixed model by a penalized spline mixed model, we develop robust EBLUPs of small area means and bootstrap estimators of MSPE. Results of a simulation study are also presented. The Canadian Journal of Statistics 42: 126–141; 2014 © 2013 Statistical Society of Canada