Preliminary Notions

Abstract

In this book we are concerned with the basic theory and methods of statistical inference and major applications such as Regression and Analysis of Variance. We will be dealing with statistical problems where it is of interest to make statistical statements about certain parameters of a population from which a set of data have been generated. It is assumed that the characteristics of interest in the population can be represented by a set of random variables and the parameters of interest are related to the distribution of the random variables. Except in Chapter 4, we shall assume that the form of the probability distribution of the random variables is known up to a set of unspecified parameters, including the parameters of interest. The statistical methods based on this assumption are called parametric methods. The methods that do not require the specification of the underlying distribution are known as nonparametric, or distribution-free methods; this is the subject of Chapter 4.