多變量分析
Multivariate Analysis
| 節 | 週三 |
|---|---|
2 09:00–09:50 | 多變量分析 A406 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
The aims of this course are: (1) To illustrate extensions of univariate statistical methodology to multivariate data. (2) To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data. (3) To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages. Topics include multivariate techniques and analyses, multivariate analysis of variance, principal component analysis, and factor analysis, cluster analysis, discrimination and classification, and machine learning. The course uses the R software for statistical computing. Students are expected to be familiar with the usage of the software.
Students are expected to have a background in undergraduate linear algebra, probability, mathematical statistics, and linear regression. Computer programming knowledge on R and/or C/C++ is required.
無備註
Class website: https://ghuang.stat.nycu.edu.tw/course/multivariate24/
The course grade will be based on 5 homework assignments (50%), 1 midterm exam (20%), and 1 final exam (30%).
Aspects of multivariate analysis
(1) introduction (2) review of linear algebra and matrices
備註：Reading (pages):\nAMSA: 1-30, 49-110
Random vectors and random sampling
(1) random vectors/matrices (2) distance (3) the sample (4) random sampling of the sample mean vector and covariance matrix (5) generalized variance (6) matrix operations of sample values
備註：AMSA: 30-37, 60-78, \n111-148\n
Multivariate normal distribution
(1) density and properties (2) sampling from multivariate normal and MLE (3) sampling distribution and large sample behavior of X and S (4) assessing the assumption of normality (5) transformation to near normality
備註：AMSA: 149-209
Inferences about a mean vector
(1) inference for a normal population mean (2) Hotelling's T2 and likelihood ratio test (3) confidence regions and simultaneous comparisons of component means (4) large sample inferences about a population mean vector
備註：AMSA: 210-238
Comparisons of several multivariate means
(1) paired comparisons and repeated measures design (2) comparing mean vectors from two populations (3) comparing several multivariate population means (one-way MANOVA)
備註：AMSA: 273-312
Principal components
(1) introduction (2) population principal components (3) summarizing sample variation by principal components (4) large sample inferences
備註：AMSA: 430-459
Factor analysis
(1) introduction (2) orthogonal factor model (3) methods of estimation (4) factor rotation (5) factor scores
備註：AMSA: 481-526
Canonical correlation analysis
(1) introduction (2) population and sample canonical variates and canonical correlations (3) sample descriptive measures of goodness
備註：AMSA: 539-563
Clustering
(1) introduction (2) similarity measures (3) hierarchical clustering methods (4) k-means clustering methods (5) multidimensional scaling
備註：AMSA: 671-715
Discrimination and classification
(1) introduction (2) separation and classification for two populations (3) classification with two multivariate normal populations (4) evaluating classification functions (5) fisher discriminant function (6) classification with several population
備註：AMSA: 575-644
Machine learning
(1) classification and regression tree (2) neural networks (3) support vector machine (4) ensemble learning
備註：ESL:\n(1) 305-317, 587-603\n(2) 389-409\n(3) 129-135, 417-438\n(4) Section 8.7, Chapter 10\n
| 週次 | 主題 |
|---|---|
| 第 1 週 | 2024-02-19(一) |
| 第 2 週 | 2024-02-26(一) |
| 第 3 週 | 2024-03-04(一) |
| 第 4 週 | 2024-03-11(一) |
| 第 5 週 | 2024-03-18(一) |
| 第 6 週 | 2024-03-25(一) |
| 第 7 週 | 2024-04-01(一) |
| 第 8 週 | 2024-04-08(一) |
| 第 9 週 | 2024-04-15(一) |
| 第 10 週 | 2024-04-22(一) |
| 第 11 週 | 2024-04-29(一) |
| 第 12 週 | 2024-05-06(一) |
| 第 13 週 | 2024-05-13(一) |
| 第 14 週 | 2024-05-20(一) |
| 第 15 週 | 2024-05-27(一) |
| 第 16 週 | 2024-06-03(一) |
| 第 17 週 | 2024-06-10(一) |
| 第 18 週 | 2024-06-17(一) |
Handouts corresponding to each lecture will be available on the class website before each class. The required textbook for this course is: Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ. (AMSA) The following book is recommended for further reading: Hastie, Tibshirani and Friedman, 2009. The Elements of Statistical Learning (2nd edition). Springer, New York, NY, USA. (ESL) Reading assignments will be made primarily in these two books.
- 地點
- A423 Joint Education Hall
- 時間
- By appointment
- 聯絡方式
- Email: ghuang@nycu.edu.tw