課程概述與目標
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.
課程大綱
|
單元主題 |
內容綱要 |
課本範圍(頁數) |
|
Aspects of multivariate analysis |
(1) introduction
(2) review of linear algebra and matrices |
1-30, 49-110 |
|
Matrix algebra and random vectors |
(1) random vectors
(2) distance
(3) sample geometry
(4) random sampling of sample mean vector and covariance matrix
(5) generalized variance
(6) matrix operations of sample values
|
30-37, 60-78,
111-148 |
|
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 |
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 |
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) |
273-312 |
|
Principal components |
(1) introduction
(2) population principal components
(3) summarizing sample variation by principal components
(4) large sample inferences |
430-459 |
|
Factor analysis |
(1) introduction
(2) orthogonal factor model
(3) methods of estimation
(4) factor rotation
(5) factor scores |
481-526 |
|
Clustering |
(1) introduction
(2) similarity measures
(3) hierarchical clustering methods
(4) k-means clustering methods
(5) multidimensional scaling |
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 |
575-644 |
參考用書
Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.
評分標準
|
項目 |
百分比 |
|
4 homework assignments |
50% |
|
Midterm exam |
20% |
|
Final exam |
30% |
