Chapter 1 - Basic Principles and Methods of Statistical Inference

Abstract

This chapter reviews some of the basic concepts and procedures of statistical inference. It discusses the likelihood function and sufficient statistics. The likelihood function for a realization from a continuous time stochastic process can be defined in an analogous way. The likelihood function forms the basis of many statistical procedures and plays a central role in the theory of inference. The frequency approach to statistical inference can broadly be described as the one wherein the performance of any statistical method is to be evaluated on the basis of hypothetical repetitions of the experiment under the same conditions. The chapter highlights the Bayesian approach to statistical inference. It discusses asymptotic inference. The chapter also discusses nonparametric methods of statistical inference.