Course Description
An introduction to the theory and methodology of multivariate statistics for students with training in linear models and mathematical statistics. Topics include the multivariate normal distribution, one and two population inference on population mean vectors, MANOVA, principal component analysis, factor analysis, discrimination, classification, and canonical correlation.
Athena Title
Multivariate Theory and Method
Equivalent Courses
Not open to students with credit in STAT 4250, STAT 6250, BIOS 8530, HPRB 8530
Prerequisite
STAT 6420 and STAT 4520/6520
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
Students will learn some basic matrix algebra for statistical use and will become familiar with the multivariate normal distribution, its properties and application, and the related distributions that arise in multivariate statistics. Students will study the multivariate linear model and learn multivariate analogs of one and two population inference on means, and the multivariate analysis of variance. Students will also learn multivariate methods for dimension reduction, classification, clustering, and other purposes. For each method, students will learn the statistical logic that explains why it works, the underlying assumptions and conditions under which the methodology can be expected to perform well, the type of questions it addresses, the results it yields, and the proper interpretation of those results. Derivations and theoretical properties will be considered for some methods. Students will learn how to implement the methods covered in the course using appropriate statistical software.
Topical Outline
Relevant vector and matrix algebra, basic multivariate statistical concepts, the multivariate normal distribution, multivariate inference for means and variance-covariance matrices in one and two population settings, multivariate analysis of variance (MANOVA), principal components, factor analysis, discriminant analysis, and canonical correlation analysis. Additional topics may be covered at the discretion of the instructor.
Syllabus