Applied Multivariate Analysis. Instructors: Dr. Amit Mitra and Dr. Sharmishtha Mitra, Department of Mathematics and Statistics, IIT Kanpur.

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September 23, 2023

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September 23, 2023

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Description

Applied Multivariate Analysis. Instructors: Dr. Amit Mitra and Dr. Sharmishtha Mitra, Department of Mathematics and Statistics, IIT Kanpur.

Multivariate analysis is a fundamental concept in applied statistics. In this course, we shall first look at basic concepts of multivariate distributions and study standard multivariate distributions which provide multivariate counterparts of the univariate distributions. Multinomial, multivariate normal, Wishart and Hotelling's T-squared distributions shall be studied in detail. Important applied multivariate data analysis concepts of principal component analysis, profile analysis, multivariate analysis of variance, cluster analysis, discriminant analysis and classification, factor analysis and canonical correlations analysis shall be covered. The theoretical concepts as well as practical data analysis using real life data shall be used to illustrate and study the concepts. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Basic Concepts on Multivariate Distribution Unlimited
  • Lecture 02 – Basic Concepts on Multivariate Distribution (cont.) Unlimited
  • Lecture 03 – Multivariate Normal Distribution I Unlimited
  • Lecture 04 – Multivariate Normal Distribution II Unlimited
  • Lecture 05 – Multivariate Normal Distribution III Unlimited
  • Lecture 06 – Some Problems on Multivariate Distributions Unlimited
  • Lecture 07 – Some Problems on Multivariate Distributions (cont.) Unlimited
  • Lecture 08 – Random Sampling from Multivariate Normal Distribution and Wishart Distribution I Unlimited
  • Lecture 09 – Random Sampling from Multivariate Normal Distribution and Wishart Distribution II Unlimited
  • Lecture 10 – Random Sampling from Multivariate Normal Distribution and Wishart Distribution III Unlimited
  • Lecture 11 – Wishart Distribution and its Properties Unlimited
  • Lecture 12 – Wishart Distribution and its Properties (cont.) Unlimited
  • Lecture 13 – Hotelling’s T-squared Distribution and its Applications Unlimited
  • Lecture 14 – Hotelling’s T-squared Distribution and Various Confidence Intervals and Regions Unlimited
  • Lecture 15 – Hotelling’s T-squared Distribution and Profile Analysis Unlimited
  • Lecture 16 – Profile Analysis Unlimited
  • Lecture 17 – Profile Analysis (cont.) Unlimited
  • Lecture 18 – Multivariate Analysis of Variance (MANOVA) I Unlimited
  • Lecture 19 – Multivariate Analysis of Variance (MANOVA) II Unlimited
  • Lecture 20 – Multivariate Analysis of Variance (MANOVA) III Unlimited
  • Lecture 21 – MANOVA and Multiple Correlation Coefficient Unlimited
  • Lecture 22 – Multiple Correlation Coefficient Unlimited
  • Lecture 23 – Principal Component Analysis Unlimited
  • Lecture 24 – Principal Component Analysis (cont.) Unlimited
  • Lecture 25 – Principal Component Analysis (cont.) Unlimited
  • Lecture 26 – Cluster Analysis: Hierarchical Clustering Unlimited
  • Lecture 27 – Cluster Analysis: Hierarchical Clustering (cont.) Unlimited
  • Lecture 28 – Cluster Analysis: Nonhierarchical Clustering Unlimited
  • Lecture 29 – Cluster Analysis Examples Unlimited
  • Lecture 30 – Discriminant Analysis and Classification I Unlimited
  • Lecture 31 – Discriminant Analysis and Classification II Unlimited
  • Lecture 32 – Discriminant Analysis and Classification III Unlimited
  • Lecture 33 – Discriminant Analysis and Classification IV Unlimited
  • Lecture 34 – Discriminant Analysis and Classification V Unlimited
  • Lecture 35 – Discriminant Analysis and Classification VI Unlimited
  • Lecture 36 – Discriminant Analysis and Classification VII Unlimited
  • Lecture 37 – Factor Analysis Unlimited
  • Lecture 38 – Factor Analysis (cont.) Unlimited
  • Lecture 39 – Factor Analysis (cont.) Unlimited
  • Lecture 40 – Canonical Correlation Analysis I Unlimited
  • Lecture 41 – Canonical Correlation Analysis II Unlimited
  • Lecture 42 – Canonical Correlation Analysis III Unlimited
  • Lecture 43 – Canonical Correlation Analysis IV Unlimited

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