ABSTRACT
This chapter presents a brief survey of the wide variety of sequential and multistage inference-procedures used in linear regression and other related models. The primary motivation behind using such methodologies in these models comes from, among other things, fixed precision inference and online (or adaptive) data-processing. After a general introduction to these models and methodologies, here we explore the significant developments in sequential and multistage fixed-precision inference in deterministic regression models, sequential shrinkage estimation in such models, and the Bayes sequential approach. These are followed by sequential inference in stochastic regression, inverse regression, and errors-in-variables models. Throughout, the emphasis is on first and second-order asymptotic properties of the procedures involved. An updated list of references is provided at the end.
