MTH514

Announcement:

Our course closely follows the book by MBK. So, I will not be uploading any specific notes. We have about SIX weeks from April 20 till May 30. An outline for the remaining course is given below.

You should closely follow the NPTEL lectures by Prof. Amit Mitra (https://nptel.ac.in/courses/111104024/), and relate to the appropriate section in MBK (stated in brackets).

Week 1. PCA (Sections 8.1-8.2); Lectures 23-25.

Week 2. Factor Analysis (Sections 9.1-9.3); Lectures 37-39.

Week 3. CCA (Sections 10.1-10.2); Lectures 40-43.

Week 4. MANOVA (Sections 12.1-12.4); Lectures 18-20.

Week 5. Multiple Correlation Coefficient (Section 6.5); Lectures 21-22.

Weeks 6 and 7. Discriminant Analysis (Chapter 11); Lectures 30-36.

Week 8. Cluster Analysis (Chapter 13); Lectures 26-29.

I have created a discussion forum on Piazza to discuss questions related to the topics mentioned above.

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General Guidelines

Class schedule : M Th F@4pm in TB111

Tutorial: W@2pm in TB111

Exam Schedule: Check DOAA

Q1 - February 7 (Friday) 4-5pm at L5

MidSem - February 22 (Saturday) 1-3pm at L5 OROS

Q2 -

Numerical Assignment - April 20, 11:59 am (morning) Discussion link (discontinued)

EndSem -

Text Book:

• Multivariate Analysis by K. V. Mardia, J. T. Kent and J. M. Bibby

References:

• An Introduction to Multivariate Statistical Analysis by T. W. Anderson
• Applied Multivariate Statistical Analysis by Richard A. Johnson and Dean W. Wichern

You can read here : 1 , 2 ,

Corrections - 1 , 2 ,

Some topics:

• Kronecker product
• Cantor distribution (also see the links here)
• Cramer-Wold and Multivariate CLT
• Multivariate Normal
• Dirichlet distribution
• Non-central chi square distribution (p.6 onwards)
• Wishart distribution
• Asymptotic normality of LRT
• 
  

Relevant Papers:

• On a Geometric Notion of Quantiles for Multivariate Data
• Fisher (1936)
• Mahalanobis (1936)
• Establishing the Positive Definiteness of the Sample Covariance Matrix
• The Non-Singularity of Generalized Sample Covariance Matrices
• PCA - 1 and 2

Assignments : 1 , 2 , 3 ,

Solutions : Quiz 1 , MidSem , Quiz 2, EndSem

Grading and Exam policy:

Mark for each exam is stated in brackets.

Quiz 1 : [10]

Mid-semester : [25]

Quiz 2 : [10]

Numerical/Homework Assignment : [15]

End-semester : [40]

Final Score = Mid-semester + Two quizzes + Graded Assignment + End-semester

Grading:

A - E : based on score quantiles

F : if score is less than or equal to 30 out of 100