This book provides a self-contained introduction of mixed-effects models and small area estimation techniques. In particular, it focuses on both introducing classical theory and reviewing the latest methods. First, basic issues of mixed-effects models, such as parameter estimation, random effects prediction, variable selection, and asymptotic theory, are introduced. Standard mixed-effects models used in small area estimation, known as the Fay-Herriot model and the nested error regression model, are then introduced. Both frequentist and Bayesian approaches are given to compute predictors of small area parameters of interest. For measuring uncertainty of the predictors, several methods to calculate mean squared errors and confidence intervals are discussed. Various advanced approaches using mixed-effects models are introduced, from frequentist to Bayesian approaches. This book is helpful for researchers and graduate students in fields requiring data analysis skills as well as in mathematical statistics.

Autorentext

Shonosuke Sugasawa is an Associate Professor in the Center for Spatial Information Science at the University of Tokyo. His research interests include Bayesian modeling, spatial statistics and mixed-effects modeling.

Tatsuya Kubokawa is a Professor in the Faculty of Economics at the University of Tokyo. His research interests include statistical decision theory, multivariate analysis and mixed-effects modeling.