Course

M482 - Multivariate Statistical Analysis

Course No:
M482
Credit:
4
Prerequisites:
M305, M306, and M205 or equivalent courses
Approval:
UG-Elective
PG-Elective
Syllabus:

Review of matrix algebra (optional), data matrix, summary statistics, graphical representations (3 hrs) Distribution of random vectors, moments and characteristic functions, transformations, some multivariate distributions: multivariate normal, multinomial, dirichlet distribution, limit theorems (5 hrs) Multivariate normal distribution: properties, geometry, characteristics function, moments, distributions of linear combinations, conditional distribution and multiple correlation (5 hrs) Estimation of mean and variance of multivariate normal, theoretical properties, James-Stein estimator (optional), distribution of sample mean and variance, the Wishart distribution, large sample behavior of sample mean and variance, assessing normality (8 hrs) Inference about mean vector: testing for normal mean, Hotelling T2 and likelihood ratio test, confidence regions and simultaneous comparisons of component means, paired comparisons and a repeated measures design, comparing mean vectors from two populations, MANOVA (10 hrs) Techniques of dimension reduction, principle component analysis: definition of principle components and their estimation, introductory factor analysis, multidimensional scaling (10 hrs) Classification problem: linear and quadratic discriminant analysis, logistic regression, support vector machine (8 hrs) Cluster analysis: non-hierarchical and hierarchical methods of clustering (5 hrs)

Reference Books:
1. K. V. Mardia, J. T. Kent, and J. M. Bibby (1980), “Multivariate Analysis”, Academic Press.
2. T. W. Anderson (2003), “An Introduction to Multivariate Statistical Analysis”, Wiley.
3. C. Chatfield and A. J. Collins (1980), “Introduction to Multivariate Analysis”, Chapman & Hall.
4. R. A. Johnson and D. W. Wichern, (2007), “Applied Multivariate Statistical Analysis”, 6th edition, Pearson.
5. Brian Everitt and Torsten Hothorn (2011), “An Introduction to Applied Multivariate Analysis with R”, Springer.
6. M. L. Eaton (1983), “Multivariate Statistics”, John Wiley.