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

15.00
Unit I: 
UNIT I

Multivariate normal distributionand 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: 
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. 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 ant its applications.

 

15.00
Unit III: 
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: 
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

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

Essential Readings: 

Books Recommended/Reference Books

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

Academic Year: 
2018-2019
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