Page 65 - Computational Statistics Handbook with MATLAB

Chapter 3

Sampling Concepts

3.1 Introduction
In this chapter, we cover the concepts associated with random sampling and
the sampling distribution of statistics. These notions are fundamental to com-
putational statistics and are needed to understand the topics covered in the
rest of the book. As with Chapter 2, those readers who have a basic under-
standing of these ideas may safely move on to more advanced topics.
In Section 3.2, we discuss the terminology and concepts associated with
random sampling and sampling distributions. Section 3.3 contains a brief dis-
cussion of the Central Limit Theorem. In Section 3.4, we describe some meth-
ods for deriving estimators (maximum likelihood and the method of
moments) and introduce criteria for evaluating their performance. Section 3.5
covers the empirical distribution function and how it is used to estimate
quantiles. Finally, we conclude with a section on the MATLAB functions that
are available for calculating the statistics described in this chapter and a sec-
tion on further readings.

3.2 Sampling Terminology and Concepts
In Chapter 2, we introduced the idea of a random experiment. We typically
perform an experiment where we collect data that will provide information
on the phenomena of interest. Using these data, we draw conclusions that are
usually beyond the scope of our particular experiment. The researcher gen-
eralizes from that experiment to the class of all similar experiments. This is
the heart of inferential statistics. The problem with this sort of generalization
is that we cannot be absolutely certain about our conclusions. However, by

© 2002 by Chapman & Hall/CRC