Stat 565: Multivariate analysis

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Stat 565: Multivariate analysis

MWF, 1:25-2:15pm, 117 Thomas Building

Prerequisite: Stat 511-514. Credits: 3

Instructor: Runze (Richard) Li, Ph.D. Office: 413 Thomas Building

Phone: 865-1555 E-mail:

Office Hours: Monday 4:00-5:00pm and Friday 10:30-11:30am

If you are unable to meet during any of these hours, please schedule an

appointment with the instructor for an alternative time.
Textbook: Anderson, T. W. (2003).An Introduction to Multivariate Statistical Analysis. 3rd Edition. Wiley, New York.
Reference Books:

1.Muirhead, R. J. (1982). Aspects of Multivariate Statistical Theory, Wiley, New York.

2. Fang, K.-T., Kotz, S and Ng, K.W. (1989). Symmetric Multivariate and Related

Distributions, Chapman and Hall, London.
3. Fang, K.-T. and Zhang, Y-T. (1990). Generalized Multivariate Analysis. Springer,

New York.

Course: This course gives an introduction to theoretical foundation for the statistical analysis of multivariate data. This course will cover theory of normal distribution, theory of estimation and hypothesis testing on mean vector and covariance matrix of multivariate normal distribution and their extension to elliptically contoured distributions. This course will cover material related to theory of discrimination, principal components, and canonical analysis. The primary goals of the course are to learn the theory of multivariate analysis, to learn applied multivariate analysis approaches and to develop theoretic problem-solving skills.
Syllabus: Course material will be covered in most sections of Chapters 1 – 12 of Anderson (2003).
Learning Object:

  1. To understand multivariate normal (multinormal) distribution theory, including multinormal definitions, marginal distribution, conditional distribution, characteristic distribution and moment generating function

  2. To understand elliptical distribution theory.

  3. To understand normal mean estimation theory

  4. To understand multinormal correlation coefficient estimation, including Pearson correlation coefficient, partial correlation coefficients and multiple correlation coefficients

  5. To understand theory related to testing hypotheses on multinormal means

  6. To understand classification theory with multinormal samples

  7. To understand theory of Wishart distribution and its applications

  8. To understand linear hypotheses in linear models.

  9. To apply likelihood ratio theory for normal linear models, for testing covariance structure in multinormal distribution.

  10. To understand theory related to principal component analysis and canonical correlation analysis.

Attendance: Attendance to each class meeting is required and beneficial.
Homework: Homework problems will be assigned when the instructors feel students ready for them. No late homeworks will be accepted except that special difficulties arise, in which case a note from a professional, such as a doctor, is necessary. Missed homeworks will be received a grade of zero. All homeworks are required. To receive credit on homework, you must show all work neatly, clearly label each problem, circle your final answers, and staple the entire assignment together in the correct order with your first and last name printed on every page. (Someone will receive a zero on a homework because (s)he didn't do one of these things and will be very unhappy -- but you were warned!) All homeworks will count as 50% of your final course grade. You are allowed, and indeed encouraged, to work with other students on the homework problems; however, verbatim copying of homework is absolutely forbidden and constitutes a violation of the academic integrity; therefore each student must ultimately produce his or her own homework to be handed in and graded.
Final exam and final project: Final exam and final project will be worth 50% of your course grade. In-class final exam portion is entirely closed-book and closed-notes, while take-home final exam portion and final project are open-book and open-notes. Any questions regarding exam grades should be taken up with the instructor. If a student has a University-approved conflict with any of the exams, (s)he must let the instructor know at least one week before the exam. A conflict exam will be scheduled to take place just before the regularly scheduled exam. Make-up exams will be given only when documentation of hospitalization, death in the family, or other emergency is provided in advance of the regularly-scheduled exam. Minor illness, such as a cold or sore throat, is not a legitimate reason for missing an exam. In the rare case that a make-up exam is necessary, the make-up exam must be taken within one week of the regularly-scheduled exam. All the exams are required, and missed exams will be received a grade of zero.
Grading policy:
Homework 50.00%

Final exam and project 50.00%

Total 100.00%
Note: Students' overall performance in class also plays an important part in evaluation, and this will be based on my subjective judgment, so the percentages are approximate.
Course web site: The instructor will use Angel to manage this course. Please check your Angel regularly and frequently.
Important University Course Administration Dates:
Please note that as a student registered for this course, you are responsible for taking care of certain administrative details before the following university-wide deadlines:

Regular Drop Deadline Wednesday, Jan. 20

Regular Add Deadline Thursday, Jan. 21 (8:00am, ET)
Final Exam Conflict Filing Period Monday-Sunday, February 15 – March 6

Late Drop Deadline Friday, April 8

Withdrawal Deadline Friday, April 29.

Final Exam May 2 – May 6.

Academic Integrity: The Academic Integrity will be observed at all times in this course.

See detailed policy at

Mutual Respect and Cooperation: The Eberly College of Science Code of Mutual Respect and Cooperation: final.pdf/view

embodies the values that we hope our faculty, staff, and students possess and will endorse to make The Eberly College of Science a place where every individual feels respected and valued, as well as challenged and rewarded

Disabilities: Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at

In order to receive consideration for course accommodations, you must contact ODS and provide documentation. If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

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