Professor JOEL OWEN B90.3303 Multivariate Statistical Analysis



 
 

office: MEC room 8-63

tel: 212-998-0446

fax: 212-995-4003

e-mail: jowen@stern.nyu.edu

office hours: to be announced

class meetings: Tuesday 6:00 to 8:50

text: Multivariate Statistical Inference and Applications by A. C. Rencher, John Wiley Publishers, 1998

prerequisite: B90.3302 (calculus-level regression course using matrix analysis)

grading policy: to be announced
 
 






SYLLABUS


 
 


I. Random Vectors and Matrices

Geometric Considerations

Mahalanobis Distance

Ellipsoids

Eigenvalues

II. Multivariate Normal Distribution

Properties

Maximum Likelihood Estimation

Distribution of y-bar and S

Wishart Distribution

Elliptically Contoured Distributions

III. Hotelling's T-sq. Tests

Tests of the Mean

Confidence Intervals

Bonferroni Intervals

IV. Discriminant Analysis

Two Groups

Several Groups

V. Classification into Groups

Two Groups

Several Groups

Estimation of Error Rates

Logistic Classification

VI. Principal Components

Properties

As Rotation of Axes

Scree Graphs

Variable Reduction Method

Information in the Small and Large Components

Relationship with Regression

VII. Factor Analysis

Factor Model

Estimation of Loadings and Communalities

Principal Factor Method

Maximum Likelihood Method

Rotations

Variable Reduction Method

Applicability of Factor Model

VIII. Canonical Correlation

Canonical Correlations and Variates

Properties

Tests of Independence

Tests of Underlying Dimensionality