多變量分析

Abstract

課程首頁

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%

授課對象：碩士生

預備知識：線性代數、機率、數學統計與線性迴歸