Multivariate Analysis

Paper Code: 
24STT322
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

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.

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT322

Multivariate Analysis

(Theory)

CO 73: Learn how to test the hypothesis regarding parameters of multivariate normal distribution. 

CO 74: Derive estimators for multivariate sampling distributions and understand the applications of partial and multiple correlation coefficients. 

CO 75: Apply Hotelling T-square, Mahanalobis D-square and Wishart distribution in multivariate sampling and also learn its usage in practical situations.

CO 76: Examine the concepts of principal component analysis and factor analysis and apply them on multivariate populations.

CO 77: Apply discriminant analysis, cluster analysis and canonical correlation analysis on different populations and their samples.

CO 78: Contribute effectively in course-specific interaction.

Approach in teaching: 

Interactive Lectures, 

Group Discussion, 

Classroom Assignment,

Problem Solving Sessions.

 

Learning activities for the students:

Assignments,

Seminar,

Presentation,

Subject based  Activities.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

18.00
Unit I: 
Multivariate Normal Distribution

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.

 

18.00
Unit II: 
Maximum Likelihood Estimation and Correlation Coefficients

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. Sample regression co-efficient and its applications.

 

18.00
Unit III: 
Hotelling's T-Square and Wishart Distribution

Hotelling-T2 and its properties and applications, Mahanalobis D2. Wishart distributions and its properties. Asymptotic distribution of Z-tanh (r). Multivariate central limit theorem.

 

18.00
Unit IV: 
Discriminant Analysis and Classification Procedures

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 populations.

 

 

18.00
Unit V: 
Multivariate Analysis Techniques

Introduction to principle component analysis, Canonical variables and canonical correlation, factor analysis, cluster analysis, basic methods and applications of MANOVA (without derivation of the distribution of wilk’s).

 

 

Essential Readings: 

·        Giri, N.C. (1977): Multivariate Statistical Inference, Academic Press.

·        Anderson, T. W. (2003): An Introduction to Multivariate Statistical Analysis, 3rd edition John Wiley.

·        Rao, C.R. (1973): Linear Statistical Inference and its Applications ,2nd edition Wiley.

·        Srivastava, M.S. and Khatri, C.G. (1970): An Introduction to Multivariate Statistics, North Holland.

 

SUGGESTED READINGS:

·        Morrison, D.F. (1976): Multivariate Statistical Methods, McGraw- Hill.

·        Nuirhead,R.J.(1982): Aspects of Multivariate Statistical Theory, John Wiley.

·        Kshirsagar, A.M. (1972). Multivariate Analysis, Marshell & Decker.

·        Roy, S.N. (1957): Some Aspects of Multivariate Analysis, John Wiley.

·        Location

·        Johnson, Richard A., Wichern, Dean W.(2007): Applied Multivariate Statistical Analysis (6th Edition), Pearson 

 

e-RESOURCES:

·        https://epgp.inflibnet.ac.in/

·        https://www.academia.edu/

·        https://www.slideshare.net/

·        https://www.youtube.com/watch?v=Ig2qF5BC8Fg&list=PL3DFCC23FCE3C7EFB

 

JOURNALS:

·        Sankhya The Indian Journal of Statistics, Indian Statistical Institute

·        Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University

·        Afrika Statistika, Saint-Louis Senega University

·        International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic

·        Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics

·        Journal of the Indian Statistical Association, Indian Statistical Association

·        Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna

·        Statistics and Applications, Society of Statistics, Computer and Applications

·        Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2024-2025
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