Applied Multivariate Analysis

This course lays the foundation of Multivariate data analysis. Most of the data sets in agricultural statistics 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.

 

  • 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. Tests of hypothesis about mean vector.
  • Wishart distribution, Hotelling’s T2 and Mahalanobis’ D2 statistics, Null distribution of Hotelling’s T2.  Rao’s U statistics and its distribution. Wilks’ λ criterion and statement of its properties. Concepts of discriminant analysis, Computation of linear discriminant function, Classification between k ( ≥2) multivariate normal populations based on LDF and Mahalanobis D2.
  • Test of hypothesis on means, Multivariate analysis of variance and covariance, Cluster analysis, Classification by linear discriminant function, Canonical correlations, Principal components, Factor analysis, multi- dimensional scaling and Correspondence Analysis. Hierarchical clustering.

 

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.