1. 多變量統計分析 Hung Chen Department of Mathematics National Taiwan University hchen@math.ntu.edu.tw 2/19/2008 https: ceiba.ntu.edu.tw?

2. 課程大綱 Matrix Algebra and Random Vectors Multivariate Normal Distribution –Random sample –Inference About a Mean Vector –Likelihood Ratio Tests, Confidence Regions Comparisons of Several Multivariate Means Principal component Analysis Factor Analysis Canonical Correlation Analysis Discrimination and Classification Clustering

3. 課程基本資訊 時間 : 星期二 9:10~10:00 星期四 11:20~13:10 地點 : 星期二新 504; 星期四 新 501 課程網址 : https://ceiba.ntu.edu.tw/962msi/ 預備知識 : Calculus, Probability (convergence concept & proof) and Math. Stat. (at least at the level of Rice’s book Mathematical Statistics and Data Analysis). Linear algebra. 課程目標 : –Learn basic techniques for analysis of multi-dimensional data. –Study multivariate distributions, especially Gaussian distribution. –Understand multivariate statistical inference and applications such as discriminant analysis and cluster analysis. –Discuss various methods for dimension reduction, including principal component analysis, factor analysis, Canonical Correlation Analysis, etc.

4. 課程基本資訊 教科書 : Johnson, R.A. and Wichern, D.W. (2007) Applied Multivariate Statistical Analysis. Pearson Prentice Hall. 評量方式 : –Homework 30%. –Midterm 35%. –Final 35%. 面談時間 : – 星期二 15:20-16:20 及 待定 課程助教林曉薇 (r93221014@ntu.edu.tw )

10. Objective: Dimension Reduction http://www.r-project.org/ 程式套件 : 安裝或載入 Flury data(swiss.heads) swiss.heads ?swiss.heads pairs(swiss.heads) Principal Components Analysis –Princomp –analysis<- princomp(~., data = swiss.heads, cor = FALSE) –screeplot(analysis) – screeplot(analysis, npcs=24, type="lines")

15. Example 1.2

17. pairs(swiss.heads)

25. Example 1.1 Scatterplot of midge data

30. Iris Data Set data(irisf) pairs(irisf[,-1])

36. Example 1.3 Wing length of Water Pipits