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.