Multivariate Analysis

Paper Code: 
STT 322
Credits: 
5
Contact Hours: 
75.00
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.

 

Students will able to

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-322

Multivariate Analysis

CO 63: Llearn how to test the hypothesis regarding parameters of multivariate normal distribution.

 

CO 64: Derive various multivariate sampling distributions and use exterior forms where appropriate, to make the necessary changes of variables.

 

CO 65: Able to apply Wishart distribution in multivariate sampling and also learn to use it in practical situations.

 

CO 66: Learn how to use various multivariate statistical methods (for example: test for significant differences between populations, use principal component analysis and factor analysis.

 

CO 67: Apply discriminant analysis, cluster analysis and canonical correlation analysis on different population and their samples.

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

 

15.00

Unit-I                                                                                                                     

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.

15.00

Unit –II                                                                                                                

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.

15.00

Unit-III                                                                                                                

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

15.00

Unit-IV                                                                                                               

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

15.00

Unit-V                                                                                                             

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)

 

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.

 

References: 

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: 
2022-2023
  • Printer-friendly version
  • PDF version