**Course Announcement**

**Time:**Monday, Wednesday, Friday at 10:00 a.m. - 10:50 a.m.

**Location:**Taft Hall 301**Instructor:**Jie Yang

**Office:**SEO 513

**Phone:**(312) 413-3748

**E-Mail:**jyang06 AT math DOT uic DOT edu

**Office Hours:**Monday, Wednesday, Friday at 12:00 p.m. - 1:00 p.m.**Textbook:**Richard A. Johnson, Dean W. Wichern,*Applied Multivariate Statistical Analysis*, Pearson Prentice Hall, 6th edition, 2007

**Reference Books:**- C. Radhakrishna Rao,
*Linear Statistical Inference and its Applications*, 2nd edition, Wiley, 1973 (Reprinted in 2001).

- T. W. Anderson,
*An Introduction to Multivariate Statistical Analysis*, 3rd edition, Wiley, 2004. - Brian Everitt, Torsten Hothorn,
*An Introduction to Applied Multivariate Analysis with R*, Springer, 2011.

**Content:**Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis

**Prerequisite:**Grade of C or better in STAT 521**Homework:**Turn in every Friday before class; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Midterms:**February 15th (Friday), and March 20th (Wednesday), 10:00 a.m. - 10:50 a.m.

**Final Exam:**May 10th (Friday), 10:30 a.m. - 12:30 p.m.

**Grading:**Homework 10%, midterms 25% each, final exam 40%

**Grading Scale:**90% A , 80% B , 70% C , 60% D**Format of All Exams:**Each exam is based on the homework and the examples discussed in class. The last class session before each exam is a review session. Please prepare any questions that you may have.*No makeup exam will be given without a valid excuse*.

- C. Radhakrishna Rao,
**Course Syllabus****WEEK****SECTIONS****BRIEF DESCRIPTION**01/14 - 01/18 1.1, 1.2, 1.3; 2.1, 2.2, 2.3; 2.5, 2.6 Aspects of Multivariate Analysis; Some Basics of Matrix and Vector Algebra, Positive Definite Matrices; Random Vectors and Matrices, Mean Vectors and Covariance Matrices 01/21 - 01/25 Holiday; 3.3, 3.5, 3.6; 4.1, 4.2 Sample Geometry and Random Sampling; Multivariate Normal Density and Its Properties 01/28 - 02/01 4.3; 4.4, 4.5; 4.6 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation; Sampling Distribution of Xbar and S, Large-Sample Behavior of Xbar and S; Assessing the Assumption of Normality 02/04 - 02/08 5.1, 5.2; 5.3; 5.4 Plausibility of mu0 as a Value for a Normal Population Mean; Hotelling's T^2 and Likelihood Ratio Tests; Confidence Regions and Simultaneous Comparisons 02/11 - 02/15 Review; 5.5; Midterm-1 exam; Large Sample Inferences about a Population Mean Vector 02/18 - 02/22 6.1, 6.2; 6.3; 6.4 Paired Comparisons and a Repeated Measures Design; Comparing Mean Vectors from Two Populations; Comparing Several Multivariate Population Means 02/25 - 03/01 6.5, 6.6; 6.7; 7.1, 7.2, 7.3 Simultaneous Confidence Intervals for Treatment Effects, Testing for Equality of Covariance Matrices; Two-Way Multivariate Analysis of Variance; Classical Linear Regression Model, Least Squares Estimation 03/04 - 03/08 7.4; 7.6; 7.7 Inferences about the Regression Model; Model Checking and Other Aspects of Regression; Multivariate Multiple Regression 03/11 - 03/15 7.7; 7A; 7.10 Multivariate Multiple Regression; Distribution of the Likelihood Ratio; Multiple Regression Models with Time Dependent Errors 03/18 - 03/22 Review; Midterm-2 exam; 8.1, 8.2 Population Principal Components 04/01 - 04/05 8.2; 8.3; 8.5, 8A Population Principal Components; Summarizing Sample Variation by Principal Components; Large Sample Inferences, Geometry of Sample Principal Component Approximation 04/08 - 04/12 9.1, 9.2; 9.3; 9.3 Orthogonal Factor Model; Methods of Estimation; Methods of Estimation 04/15 - 04/19 10.1, 10.2; 10.3; 10.4 Canonical Variates and Canonical Correlations; Interpreting the Population Canonical Variables; Sample Canonical Variates and Sample Canonical Correlations 04/22 - 04/26 11.1, 11.2; 11.3; 11.4 Introduction, Separation and Classification for Two Populations; Classification with Two Multivariate Normal Populations; Evaluating Classification Functions 04/29 - 05/03 11.6, 11.7; Review; Review Fisher's Method for Discriminating, Logistic Regression and Classification 05/06 - 05/10 Exam week (Final exam)

**Homework**- Homework #1, due 01/25/2019

- Homework #2, due 02/01/2019

- Homework #3, due 02/08/2019

- Homework #4, due 02/22/2019

- Homework #5, due 03/01/2019

- Homework #6, due 03/08/2019

- Homework #7, due 03/18/2019

- Homework #8, due 04/05/2019

- Homework #9, due 04/12/2019

- Homework #10, due 04/22/2019

- Homework #11, due 05/01/2019

- Homework #1, due 01/25/2019
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