Asymptotic Analysis of Estimating Functions

The area of estimating functions has wide applications and has

undergone rapid development during the recent years. As a theory, it

is sufficiently general to include most of the important aspects of

the classical theory of statistical inference and to accomodate a

variety of the more recent themes such as the Generalized Linear

Models (GLM), the Generalized Estimating Equations (GEE), the

Generalized Linear Mixed Effect Models (GLMM), the various forms of

Autoregressive Conditionally Heteroscedastic models (ARCH), the

Restrictive Maximum Likelihood (REML), the Empirical Likelihood, as

well as many estsimators in Surivval Analysis, Nonparametric

Regression, and Spatial Statistics. By the constructive nature of this

theory, it will no doubt also provide us with the insights to derive

new statistical procedures for scientific problems that will arise.

Yet, these advantages do not make the subject more difficult to

understand, for it is built on a handful of elementary tools such as

linearization and projection, which apply repeatedly at different

levels of sophistication.