Robust prediction from linear mixed-effects models with applications to small area estimation

Linear mixed-effects models have a wide range of applications. However when the observed response variable and/or the covariate information is contaminated, even the predictors which only depend on the first two moments of the random terms in the model, such as the Best Linear Unbiased Prediction (BLUP), can have a larger than acceptable prediction error due to the contamination. Various robust statistical methods aiming at the reduction of the influence of the contaminated data on the linear mixed-effects model parameter estimations have been proposed recently, among them is the method of bounded influence. So far the application of this method has been on the estimation, not prediction from the model. In this research, I studied possibility of extending the application of bounded influence method to prediction. I proposed a prediction method which limits the influence from both the contamination coming from response variable Y and the covariate X through bounded influence functions. The asymptotic distribution of a Small Area Estimator is also derived. The proposed bounded influence predictor is fairly efficient when data is not contaminated and is more efficient than the Best Linear Unbiased Predictor (BLUP) when data is contaminated. I applied these predictors to the Small Area Estimation problem in crop area survey. Statistical properties are further studied and demonstrated through a simulation study, in which a variety of contamination patterns may occur in practice are considered.