I.The Basic Information of the Course(Time New Rome, 12 points, bold font)
Course Number:202012420031
The English Name of the Course：Multivariate Statistical Analysis
The Chinese Name of the Course：多元统计分析
In-class Hours and Allocation:total class hours:32, classroom teaching:30classhours, classroom discussion:2classhours
Credit(s):2
Semester:2
Applied Discipline：Science and Engineering Discipline
Course Object Oriented：Master,Doctor
Evaluation Mode:ProcessEvaluation.
Teaching Method:Seminar Teaching,CaseTeaching,BlendedTeaching
Course Opening Department:Mathematics and Science College
II.Prerequisite Course( Time New Rome 12 points bold font)
Calculus,Linear algebra,Probability theory and mathematical statistics, etc
III. The Objectives and Requirements of the Course(Time New Rome 12 points, total words: about 200 words)
The aim of the courseis to let the graduate studentsgraspthe basic ideas, theories and methodsofmultivariate statistical analysis, andhave the ability to applythe relative methods tosolveproblems.
By learning this course, students can master the basic analysis methods of multivariate statistical analysis, and understand the development direction and Prospect of disciplines related to statistical analysis
IV. The Content of the Course
Chapter 1Multivariate normal distribution(6 classhours)
1.1Random vector and related concepts
1.2multivariate normal distribution
1.3conditional distribution and correlation of normal vector
1.4some properties of normal random matrix
1.5quadratic form of normal vector
1.6Wishart distribution and its properties
Chapter 2 Parameter estimation of multivariate distribution（4 classhours）
2.1Estimationsofmean vector and covariance matrix of normal distribution
2.2 Maximum likelihood estimationsof generalized variance and correlation coefficient of normal distribution
2.3 Parameter estimation of multivariate distribution
Chapter 3 Statistical hypothesis test (4 class hours)
3.1General hypothesis test and likelihood ratio test statistics
3.2 Testsof mean vector of normal population when covariance matrix is known
3.3 Testsof mean vector of normal population when covariance matrix is unknown
3.4 Testsof constrained mean vector of normal population
3.5 Large sample extrapolation of general mean
3.6 Testsof covariance matrix of normal population
Chapter 4 Multivariate linear statistical model(4 class hours)
4.1 MLE estimation and prediction of parameters of normal regression model
4.2 Least square estimation and properties of parameters of linear regression model
4.3 Parameter estimation and properties of generalized linear regression model
4.4 Hypothesis test of parameters of normal regression model
Chapter 5 Discriminant analysis (4 class hours)
5.1 Distance discrimination
5.2 Bayes discrimination
5.3 Fisher discrimination
5.4 Exercises
Chapter 6 Principal component analysis (4 class hours)
6.1 Basic idea
6.2 Application of principal component analysis
6.3 Principal component analysis of multivariate population and its estimation and test
6.4 Exercises
Chapter 7 factor analysis (3 class hours)
7.1 Basic factor analysis model
7.2 Basic properties of factor model
7.3 Solution of factor model, factor score, maximum orthogonal rotation of variance
7.4 Exercises
Chapter 8 cluster analysis（3 class hours)
8.1 Basic idea
8.2 Similarity and distance
8.3 System clustering
8.4 Exercises
In the aspect of Ideological and political courses, by citing the actual economic data of our country as an example, this course introduces the important progress of national economic development in the process of case teaching, and promotes the spirit of patriotism. Two cases are introduced in the course of teaching
Case 1: China's economic development has been growing steadily since 1978. As we all know, 1978 is the starting point of China's reform and opening up. Since the Third Plenary Session of the 11th CPC Central Committee, China has become the world's second largest economy and entered the ranks of upper middle income countries after 40 years of magnificent and extraordinary course. In the past 40 years, China has achieved leapfrog development in economic structure, finance, infrastructure, medical and educational level, and sustainable development.
Case 2: Academician Xiru Chen (1934.2.11-2005.8.8)
Xiru Chen obtained a series of important results in the field of large sample theory of linear regression. In the field of parametric statistics and non-parametric statistics, we have done some work with international influence. In this paper, the existence and form of sequential mini-max equivariant estimators for location scale parameters under general identical loss are solved. The conditions for accurate interval estimation of general parameters as distribution functionals under various sampling mechanisms (fixed, two-stage and sequential) are given. Some conjectures about this problem by foreign scholars are negated, and the non approximation of U-statistics to normal distribution is solved The problem of uniform convergence rate. In recent years, some important achievements have been made in the study of linear regression models with errors in independent variables and generalized linear models.
V. Reference Books, Reference Literatures, and Reference Materials
A. Text Books, Monographs and References
1.张润楚.多元统计分析，科学出版社，2019.12.
2.T.W.Anderson.多元统计分析导论(第三版）.人民邮电出版社，2010.
3.王学民.应用多元统计分析，第五版.上海财经大学出版社，2017.8
4. Wolfgang Hardle, Leopold Simar. Applied Multivariate Statistical Analysis. Springer-Verlag Berlin Heidelberg, 2003.
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