Theory and Methods of Statistics

4

Basic Concepts of Statistical Inference

Abstract

The basic concepts of statistical inference are introduced and three main problems are stated, namely, Point Estimation, Hypothesis Testing, and Construction of Confidence Sets. This is followed by a unified approach of Statistical Decision Theory. We then discuss Sufficient Statistics and the Factorization Theorem. Finally, the issue of optimality is approached in several ways, which are pursed in subsequent chapters.

Keywords

Parametric and Nonparametric Models; Sufficient Statistics; Bayes Rules; Minimax Rules; Admissibility

4.1 Population and Random Samples

The term “Statistics” is commonly used as a synonym for data, but “Statistical Inference” is the science of analyzing data to probe ...