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