Robust Small Area Estimation
J.N.K. Rao, Carleton University
Abstract: Small area estimation has been extensively studied under linear mixed models,
in particular unit level linear mixed models. Empirical best linear unbiased prediction
(EBLUP) estimators of small area means have been developed along with nearly unbiased
estimators of mean squared errors. However, the EBLUP estimators can be sensitive to
outliers. In this talk, I will first present a robust EBLUP type method for small area
estimation and demonstrate its advantage over the customary EBLUP under the unit level
linear mixed model in the presence of outliers in the random small area effects and/or
unit level errors. I will also study a bootstrap method of estimating the mean squared
error of the robust EBLUP type estimator. Secondly, I will relax the assumption of linear
regression model for the fixed part of the linear mixed model and replace it by the weaker
assumption of a penalized spline regression model and develop robust EBLUP type estimators
of small area means in the presence of outliers in the random small area effects and /or
unit level errors. I will also discuss
bootstrap estimators of mean squared error. Simulation results and applications to real
data will also be presented.