Probability for statisticians - 2000 (Galen R. Shorack)

Được đăng lên bởi bocau
Số trang: 599 trang   |   Lượt xem: 6288 lần   |   Lượt tải: 0 lần
Probability for

Galen R. Shorack


There is a thin self-contained textbook within this larger presentation.
To be sure that this is well understood, I will describe later how I have used this
text in the classroom at the University of Washington in Seattle.
Let me first indicate what is different about this book. As implied by the
title, there is a difference. Not all the difference is based on inclusion of statistical
material. (To begin, Chapters 1–6, provide the mathematical foundation for the
rest of the text. Then Chapters 7–8 hone some tools geared to probability theory,
while Chapter 9 provides a brief introduction to elementary probability theory right
before the main emphasis of the presentation begins.)
The classical weak law of large numbers (WLLN) and strong law of large numbers
(SLLN) as presented in Sections 10.2–10.4 are particularly complete, and they also
emphasize the important role played by the behavior of the maximal summand.
Presentation of good inequalities is emphasized in the entire text, and this chapter
is a good example. Also, there is an (optional) extension of the WLLN in Section
10.6 that focuses on the behavior of the sample variance, even in very general
Both the classical central limit theorem (CLT) and its Lindeberg and Liapunov
generalizations are presented in two different chapters. They are first presented in
Chapter 11 via Stein’s method (with a new twist), and they are again presented in
Chapter 14 using the characteristic function (chf) methods introduced in Chapter
13. The CLT proofs given in Chapter 11 are highly efficient. Conditions for both
the weak bootstrap and the strong bootstrap are developed in Chapter 11, as is
a universal bootstrap CLT based on light trimming of the sample. The approach
emphasizes a statistical perspective. Much of Section 11.1 and most of Sections
11.2–11.5 are quite unusual. I particularly like this chapter. Stein’s method is also
used in the treatment of U-statistics and Hoeffding’s combinatorial CLT (which
applies to sampling from a finite population) in the optional Chapter 17. Also, the
chf proofs in Section 14.2 have a slightly unusual starting point, and the approach
to gamma approximations in the CLT in Section 14.4 is new.
Both distribution functions (dfs F (·)) and quantile functions (qfs K(·) ≡ F−1 (·))
are emphasized throughout (quantile functions are important to statisticians). In
Chapter 7 much general information about both dfs a...
Probability for
Galen R. Shorack
Probability for statisticians - 2000 (Galen R. Shorack) - Trang 2
Để xem tài liệu đầy đủ. Xin vui lòng
Probability for statisticians - 2000 (Galen R. Shorack) - Người đăng: bocau
5 Tài liệu rất hay! Được đăng lên bởi - 1 giờ trước Đúng là cái mình đang tìm. Rất hay và bổ ích. Cảm ơn bạn!
599 Vietnamese
Probability for statisticians - 2000 (Galen R. Shorack) 9 10 663