Changes for Seventh Edition
In the preparation of this seventh edition, our goal has remained steadfast: to
produce an outstanding text in mathematical statistics. In this new edition, we have
added examples and exercises to help clarify the exposition. For the same reason, we
have moved some material forward. For example, we moved the discussion on some
properties of linear combinations of random variables from Chapter 4 to Chapter
2. This helps in the discussion of statistical properties in Chapter 3 as well as in
the new Chapter 4.
One of the major changes was moving the chapter on “Some Elementary Statistical
Inferences,” from Chapter 5 to Chapter 4. This chapter on inference covers
confidence intervals and statistical tests of hypotheses, two of the most important
concepts in statistical inference. We begin Chapter 4 with a discussion of a random
sample and point estimation. We introduce point estimation via a brief discussion
of maximum likelihood estimation (the theory of maximum likelihood inference is
still fullly discussed in Chapter 6). In Chapter 4, though, the discussion is illustrated
with examples. After discussing point estimation in Chapter 4, we proceed
onto confidence intervals and hypotheses testing. Inference for the basic one- and
two-sample problems (large and small samples) is presented. We illustrate this
discussion with plenty of examples, several of which are concerned with real data.
We have also added exercises dealing with real data. The discussion has also been
updated; for example, exact confidence intervals for the parameters of discrete distributions
and bootstrap confidence intervals and tests of hypotheses are discussed,
both of which are being used more and more in practice. These changes enable
a one-semester course to cover basic statistical theory with applications. Such a
course would cover Chapters 1–4 and, depending on time, parts of Chapter 5. For
two-semester courses, this basic understanding of statistical inference will prove
quite helpful to students in the later chapters (6–8) on the statistical theory of
inference.
Another major change is moving the discussion of robustness concepts (influence
function and breakdown) of Chapter 12 to the end of Chapter 10. To reflect
this move, the title of Chapter 10 has been changed to “Nonparametric and Robust
Statistics.” This additional material in the new Chapter 10 is essentially the important
robustness concepts found in the old Chapter 12. Further, the simple linear
model is discussed in Chapters 9 and 10. Hence, with this move we have eliminated Chapter 12.
Additional examples of R functions are in Appendix B to help readers who want
to use R for statistical computation and simulation. We have also added a listing
of discrete and continuous distributions in Appendix D. This will serve as a quick
and helpful reference to the reader.