MH4501 · Previously taught undergraduate course

Multivariate Analysis

Undergraduate Mathematical Sciences

Spring, 2017–2018 & 2020–2023Back to teaching history

Historical course page. Course materials and assessment information for registered students are provided through NTULearn. External resource links may require NTU access.

Overview

This is a 4AU (academic unit) statistics course and suitable for third- or fourth-year undergraduate students, who have learned Linear Algebra, Multivariate Calculus, Probability, Univariate Statistics, and Regression Analysis (optional but preferred). This course will cover the basic multivariate statistical inference and main statistical tools for exploratory data analysis and dimension reduction.
For those who need to apply waiver requests, please refer to the rules stated at the bottom of this page.

Learning Objectives and Outcomes

This course focuses on the standard methods of multivariate statistical analysis. Many essential data analysis techniques, such as principal component analysis and discriminant analysis, will be covered. This course equip students with the necessary skills for being data analysts.
Upon successful completion of this course, the students will be able to:

Analyze multivariate data and the dependence structure of variates to extract the useful information from a massive dataset;
Apply suitable tools for exploratory data analysis, dimension reduction, and classification to formulate and solve real-life problems;
Implement the multivariate analysis techniques with statistical software such as R in a manner that the methodology adopted is motivated by appropriate statistical theory.

Assessment Scheme

Take-home Assignments (15%)

In-class Midterm Examination (25%)

Centralized Final Examination (60%)

Topics

[2hrs] Population and Sample Statistics
[3hrs] Multivariate Normal Distribution
[4hrs] Multivariate Inference
[3hrs] Multivariate Analysis of Variance (MANOVA)
[3hrs] Clustering Analysis (CA)
[4hrs] Principal Component Analysis (PCA)
[4hrs] Factor Analysis (FA)
[3hrs] Canonical Correlation Analysis (CCA)
[3hrs] Discriminant Analysis (DA)
[If time permits] Further topics: Independent Component Analysis (ICA)

References

[Textbook] R. A. Johnson and D. W. Wichern. (2007) Applied Multivariate Statistical Analysis (6th Edition). Pearson.

W.K. Härdle and L. Simar. (2015) Applied Multivariate Statistical Analysis (4th Edition). Springer.

T. W. Anderson. (2003) An introduction to Multivariate Statistical Analysis (3rd Edition). Wiley

Waiver Requests by NTU Singapore Students

Prerequisites: MH2500 (Probability & Introduction to Statistics); MH3500 (Statistics); MH3510 (Regression Analysis)
Rules for Prerequisite Waiver Requests: There is no way to approve the waivers of MH2500 and MH3500. MH3510 can be waived subject to good academic records.
Rules for Timetable Clash Waiver Requests: Students have to provide valid reason(s) for how they catch up the progress. Moreover, they need to provide a solution to how can they attend the midterm examination in the week after the recess week.
Important Message: Even though your waiver requests are approved, it does not mean that your current knowledge allows you to handle this course easily or missing some lectures/tutorials/labs does not matter. Instead, I trust in you that you are able to self-acquire the pre-requisitie knowledge and will catch up the progress by yourself.