**DESCRIPTION OF COURSES**

**AS 567 APPLIED MULTIVARIATE ANALYSIS (2L+1P) I
(Pre-requisite : AS 560, AS 561, AS 562, AS 563)**

**Objective**

This course lays the foundation of multivariate data analysis. Most of the data sets in agricultural sciences are multivariate in nature. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of agricultural research data, its presentation and analysis.

**Theory**

UNIT I

Multivariate normal distribution, marginal and conditional distribution, Concept of random vector, its expectation and variance-covariance matrix. Marginal and joint distributions. Conditional distributions and Independence of random vectors. Multinomial distribution. Sample mean vector and its distribution. Maximum likelihood estimates of mean vector and dispersion matrix.

UNIT II

Wishart distribution, Hotelling’s T2 and Mahalanobis’ D2 statistics, Null distribution of Hotelling’s T2. Tests of hypothesis about mean vector. Rao’s U statistics and its distribution. Wilks’ λ criterion and statement of its properties. Multivariate analysis of variance and covariance.

UNIT III

Concepts of discriminant analysis, computation of linear discriminant function (LDF), classification between k multivariate normal populations based on LDF and Mahalanobis D2. Cluster analysis: k-means and Hierarchical clustering. Canonical correlations, Principal components, Factor analysis, multi-dimensional scaling and Correspondence Analysis.

**Practicals**

Maximum likelihood estimates of mean-vector and dispersion matrix. Testing of hypothesis on mean vectors of multivariate normal populations. Cluster analysis, Discriminant function, Canonical correlation, Principal component analysis, Factor analysis. Multivariate analysis of variance and covariance, multidimensional scaling.

**Suggested Readings**

- Anderson, T.W. 1984.
*An Introduction to Multivariate Statistical Analysis*. John Wiley. - Arnold, Steven F. 1981.
*The Theory of Linear Models and Multivariate Analysis*. John Wiley. - Chatfield, C. and Collins, A.J. 1982.
*Introduction to Multivariate Analysis*. Prentice Hall. - Giri, N.C. 1977.
*Multivariate Statistical Inference*. Academic Press. - Johnson, R.A. and Wichern, D.W. 1988.
*Applied Multivariate Statistical Analysis*. Prentice Hall. - Kshirsagar, A.M. 1972.
*Multivariate Analysis*. Marcel Dekker. - Muirhead, R.J. 1982.
*Aspects of Multivariate Statistical Theory*. John Wiley. - Rao, C.R. 1973.
*Linear Statistical Inference and its Applications*. John Wiley. - Rencher, A.C. 2002.
*Methods of Multivariate Analysis*. John Wiley. - Srivastava, M.S. and Khatri, C.G. 1979.
*An Introduction to Multivariate Statistics*. North Holland.