Some new models for small area estimation

This dissertation includes some new models for small area estimation. There are four parts in total. The first part studied the selection of fixed effects covariates in linear mixed models. A modified bootstrap selection procedure for linear model from literature was extended to linear mixed effects models. Both theoretical work and simulations showed the effectiveness of this procedure for linear mixed effects models.;In the second part, a new approach by shrinking both means and variances of small areas was introduced. This method modeled the small area means and variances in a unified framework. The smoothed variance estimators used information of direct point estimators and their sampling variances, and consequently, for the smoothed small area estimators. Conditional mean squared error of prediction was also studied in this part to evaluate the performance of predictors.;The third part studied the confidence intervals of small area estimators introduced in the second part. The literature of small area estimation is dominated by point estimation and their standard errors. The standard normal or student-t confidence intervals do not produce accurate intervals. The confidence intervals produced in this part are from a decision theory perspective.;The fourth part estimated the small areas means with clustering of the small areas. In the realistic application, the estimation may not be appropriate to "borrow strength" from all other small areas universally, if cluster effects exist between clusters of small areas. A model based on clustering was studied in this part, which included an additional cluster effect to the basic area level model. Since the partition of clusters was not known, a stochastic search procedure from literature was adapted first to find the clustering partition.