STAT 141 - Multivariate Theory
Course Description
Multivariate normal distribution; inference on the mean vector and dispersion matrix;
comparing two normal populations; multivariate analysis of variance and covariance
Course Learning Outcomes
After completion of the course, the student should be able to:
- Recognize the need for and importance of multivariate theories in making inferences about one or more
populations;
- Derive properties of multivariate distributions;
- Apply statistical procedures in making inferences about one or more populations; and
- Interpret correctly the results after completing the analysis.
Course Outline
Unit 1. Preliminaries and Introduction
- Introduction to the Course
- Aspects of Multivariate Analysis
- Matrix Algebra and Random Vectors
- Sample Geometry and Random Sampling
Unit 2. Multivariate Normal Distribution (MVN)
- Definition
- Theorems on Multivariate Normal Distribution
Unit 3. Other Multivariate Distributions
- Wishart Distribution
- Hotelling’s T2 Distribution
Unit 4. Inferences for the Multivariate Normal Mean Vector
- Introduction
- Testing for the Mean
- Confidence Intervals for the Mean
Unit 5. Comparing Two Normal Populations
- Test for Equal Means Assuming Equal Dispersion Matrices
- Test for Equal Means Assuming Unequal Dispersion Matrices
- Paired Comparison
Unit 6. Multivariate Analysis of Variance
- One-Way Classification
- Two-Way Classification