Multivariate Statistical Analysis

Department: 
MATH
Course Number: 
6267
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every spring semester

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

Prerequisites: 

MATH 4261, MATH 4262 or equivalent and MATH 6241

Course Text: 

At the level of Anderson, An Introduction to Multivariate Statistical Analysis, and Tong, The Multivariate Normal Distribution

Topic Outline: 
  • Multivariate Normal Distribution Theory
    • Joint, marginal, and conditional distribution; distributions of linear functions and quadratic forms of multivariate normal random variables
  • Correlation Analysis, Linear Regression, and Predication
    • Simple correlation, partial correlation, multiple correlation, linear regression equation, best prediction function and best linear predication function
  • Sampling Distributions
    • Sampling distributions for the mean vector and for the various correlation coefficients, partitioning of sum of squares, Hotelling's T2 distribution, the Wishart distribution
  • Introduction to Multivariate Probability Inequalities via Dependence and Heterogeneity
  • Estimation of Parameter Vectors via applications of the results on the topics in (3) and (4) above, especially for elliptical and rectangular confidence regions
  • Hypotheses Testing for Parameter Vectors
  • Multivariate Discriminant Analysis and Classification Theory, with Specific Applications to Medicine and Pattern Recognition
  • Applications to Multivariate Quality Control and Process Control via Applications of Results on the topics in (3), (4) and (6) above.