课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAT7102
概率统计专题
MAT7102 Topics in Probability and Statistics
2.
课程性质
Compulsory/Elective
专业选修课 Major Elective Courses
3.
课程学分/学时
Course Credit/Hours
3/48
4.
授课语言
Teaching Language
英文 English
5.
授课教师
Instructor(s)
邵启满 讲席教授 Chair Professor Qiman Shao
6.
是否面向本科生开放
Open to undergraduates
or not
是 Open to undergraduates
7.
先修要求
Pre-requisites
（如面向本科生开放，请注明区分内容。
If the course is open to
undergraduates, please indicate the difference.）
数理统计（MA204） Mathematical Statistics（MA204）
8.
教学目标
Course Objectives
本课程介绍了某些统计概念和概率统计方法，这些概念和方法对研究生在准备研究论文时是非常有用
的。该课程着重介绍最新的概率统计技术在实际中的应用以及它们的基本理论。
This course introduces some basic concepts and methods in probability and statistics,
which are potentially useful for graduate students in preparing their research papers
in
probability and statistics. Focus is on applications of state-of-the-art probabi
lity
and statistical techniques and their underlying theory.
9.
教学方法
Teaching Methods
讲授 Lectures
10.
教学内容
Course Contents
Section 1
基本的渐近方法：收敛性；大数定律；中心极限定理；
delta
方法；
Edgeworth 展开。（6 hours）
Basic asymptotic method
s: convergence; stochastic orders; laws of large
numbers; central limit theorems; delta method; Edgeworth expansions.
(6
hours)
Section 2
稳健方法：稳健性度量；
M
估计量
；
L
估计量；
R
估计量。（
6 hours
）
Robust methods: measures of robustness; M-estimator; L-estimator; R-
estimator. (6 hours)
Section 3
基本概率统计不等式。（
10 hours
）
Fundamental inequalities in probability and statistics. (10 hours)
Section 4
分布函数的逼近方法，斯坦因方法。（
13 hours
）
Approximation method for distribution functions, Stein’s method. (13 hours)
Section 5
学生化统计量的渐近性质。（
13 hours
）
Asymptotic theory of studentlized statistics. (13 hours)
Section 6
Section 7
Section 8
Section 9
Section 10
…………
11.
课程考核
Course Assessment
（○
1
考核形式
Form of examination
；○
2 .
分数构成
grading policy
；○
3
如面向本科生开放，请注明区分内
容。 If the course is open to undergraduates, please indicate the difference.）
课堂表现 Class Performance 10%
平时作业 Assignments 30%
期末考试
Final Exam 60%
12.
教材及其它参考资料
Textbook and Supplementary Readings
In this course, no single textbook can cover all the topics. Relevant references are as follows:
[1] Shao, J. (1999). Mathematical Statistics. Springer: New York.
[2]de la Pe˜na, V., Lai, T. L., Shao, Q. M. (2009). Self-
normalized Processes: Limit Theory and Statistical
Applications. Springer Series in Probability and its Applications, Springer-Verlag, New York.
[3]Chen, L. H. Y., Goldstein, L. and Shao, Q. M. (2011). Normal Approximation by Steins Me
thod. Springer
Series in Probability and its Applications, Springer-Verlag, New York.
[4]DasGupta, A. (2008). Asymptotic Theory of Statistics and Probability. Springer: New York.
