Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur, Kanpur - 208016 (India)
MTH 314A : Multivariate Analysis
Prerequisites: MTH211A (Theory of Statistics) or MTH418A (Inference 1)
Syllabus:
Basic properties of random vector: CDF and PDF of random vectors -
Moments - Characteristics functions Orthogonal and Polar transformations
Generalization of univariate distribution (Multinomial, Dirichlet).
Normal Distribution Theory: Normal data matrix (NDM): characterization
and properties Linear forms - Transformation of NDMs, Wishart Distribution, The
Hotelling's T2 Distribution
Estimation and Testing: Maximum likelihood estimation Likelihood
ratio test - Union intersection test Simultaneous confidence intervals.
Multivariate Analysis of Variance (MANOVA): Formulation of multivariate
one-way classification Likelihood ratio principle
Principal Component Analysis: Principal components - Sampling properties
of principal components - Principal component projections.
Factor Analysis: The factor model - Principal factor analysis - Maximum
likelihood factor analysis - Goodness of fit - rotation of factors - factor
scores
Canonical correlation analysis: Population and sample canonical
correlation vectors, variables and coefficients and their properties.
Discrimination Analysis: Fisher's LDA - QDA - Probabilities of
misclassification
Cluster Analysis: Distances and similarities - Hierarchical methods -
K-means method
Books to be followed:
Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis. United Kingdom: Wiley.
Johnson, R. A., Wichern, D. W. (2019). Applied Multivariate Statistical
Analysis. United Kingdom: Pearson
Other
References:
Mardia, K. V., Bibby, J. M., Kent, J. T. (1979). Multivariate Analysis.
United Kingdom: Academic Press.
Muirhead, R. J. (2009). Aspects of Multivariate Statistical Theory. Germany: Wiley.
Hastie, T., Friedman, J., Tibshirani, R. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Germany: Springer New York.
Brenner, D., Bilodeau, M. (1999). Theory of Multivariate Statistics. Germany: Springer.
B.S. Everitt, S.
Landau, M. Leese, D. Stahl. Cluster Analysis, Wiley.
Course Policy: Earn your marks and grades. I will be the happiest instructor to award the best grades to all the students.
Grading Scheme: Quiz- 30%, Mid Sem.- 30% End Sem.- 40%
Contact hours: 24 X 7, by email, phone, what's app. (If possible and not so urgent, avoid calling between 12-7 AM.)
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