Multivariate Normal Distribution, Wishart distribution and their properties, Hotelling’s T^2 Distribution, Methods of Estimation; Maximum Likelihood and least squares, Multivariate Hypothesis testing, Likelihood ratio test, One sample and multi-sample hypothesis. Principal Component Analysis, Factor Analysis, Discriminant Analysis.
Canonical Correlation, Cluster analysis, Path analysis, Multivariate Analysis of variance (MANOVA).
To impart the conceptual and advanced knowledge of multivariate data. To teach various advanced techniques to handle the challenges presented by these data. To develop sound knowledge of multivariate theories and its application in different fields.
Course Learning Outcomes
On completion of the course students should be able to:
• Understand multivariate statistical analysis, both theory and methods.
• Have an understanding of the link between multivariate techniques and corresponding univariate techniques.
• Undertake multivariate hypothesis tests, and draw appropriate conclusions.
• Recognition of the variety of advanced multivariate techniques and their proficient applications.
• Development of the skill to summarize, analyze and interpret the multivariate data.
• Use different softwares to analyze multivariate data.
Covariance Matrix Of a Random Vector by Neal Patwari
Introduction to Eigenvalues and Eigenvectors - Part 1
Finding Eigenvalues and Eigenvectors : 2 x 2 Matrix Example
Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14
Principal Component Analysis (PCA) by Steve Brunton
Principal Component Analysis (PCA): Illustration with Practical Example in Minitab
Factor Analysis - an introduction by Ben Lambert
Factor Analysis - Factor Loading, Factor Scoring & Factor Rotation (Research & Statistics)
Factor Analysis Using SPSS by Dr. Todd Grande
Introduction to One-Way Multivariate Analysis of Variance (One-Way MANOVA)
Conducting a MANOVA in SPSS with Assumption Testing
Multi-factor ANOVA (Minitab) by Oxford Academic (Oxford University Press)
Book Title : Applied Multivariate Statistical Analysis
Author : Richard A. Johnson, Dean W. Wichern
Edition : 6th Edition
Publisher : Pearson Prentice Hall
Title : Random Vectors
Type : Reference Book
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Title : Eigen Vaues and Eigen Vector
Type : Reference Book
View Eigen Vaues and Eigen Vector
Title : Finding Eigen Values
Type : Other
View Finding Eigen Values