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Multivariate Analysis
This course lays the foundation of Multivariate data analysis. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters.
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Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
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Paper Code |
Paper Title |
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STT-322 |
Multivariate Analysis |
CO 55: Able to derive various multivariate sampling distributions and use exterior forms where appropriate, to make the necessary changes of variables. Understand and be able to use Kronecker products in problems related to the multivariate normal distribution.
CO 56: Understand how the Wishart distribution arises in multivariate sampling and how to use it.
CO 57: Understand how to use various multivariate statistical methods (for example: test for significant differences between populations, use principalcomponent analysis and factor analysis, discriminant analysis, cluster analysis and canonicalcorrelation analysis)
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Approach in teaching:
Interactive Lectures, Group Discussion, Classroom Assignment Problem Solving Sessions
Learning activities for the students:
Assignments Seminar Presentation Subject based Activities
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Classroom Quiz Assignments Class Test Individual Presentation |
Multivariate normal distribution and bivariate normal distribution- marginal and conditional distributions, joint distribution of linear function of correlated normal variates. Characteristic function of multivariate normal distribution. Distribution of quadratic forms.
Maximum likelihood estimator of the mean vector and covariance, their independence and related distributions. Null and non-null distribution of partial and multiple correlation coefficients. Multiple and partial regression, examine the multiple regression equation, concept of weighted least square, regression equation on grouped data, various methods of selecting the best regression equation. Sample regression co-efficient and its applications.
Hotelling-T2 and its properties and applications, Mahanalobis D2. Wishart distributions and its properties. Asymptotic distribution of Z-tanh (r).Multivariate central limit theorem.
Classification and discrimination procedure for discrimination between two multivariate normal populations, sample discriminate function, test associated with discriminate functions probabilities of misclassification and their estimation. Classification into more than two multivariate normal population.
Introduction to principle component analysis, Cannonical variables and canonical correlation, factor analysis, cluster analysis, basic methods and applications of MANOVA(without derivation of the distribution of wilk’s)
1. Giri, N.C. (1977): Multivariate Statistical Inference, Academic Press.
2. Anderson, T .W. (1984): An Introduction to Multivariate Statistical Analysis, 2nded, John Wiley.
3. Rao, C.R. (1973): Linear Statistical Inference and its Applications ,2 nded, Wiley.
4. Srivastava, M.S. and Khatri, C.G. (1970): An Introduction to Multivariate Statistics, North Holland.
5. Morrison, D.F. (1976): Multivariate Statistical Methods, McGraw- Hill.
6. Nuirhead,R.J.(1982): Aspects of Multivariate Statistical Theory, John Wiley.
7. Kshirsagar, A.M. (1972). Multivariate Analysis, Marshell & Decker.
8. Roy, S.N. (1957): Some Aspects of Multivariate Analysis, John Wiley.
Location
9. Johnson, Richard A., Wichern, Dean W.(2007): Applied Multivariate Statistical Analysis (6th Edition), Pearson
