**Course Announcement**

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

**Location:**Taft Hall 216**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 11:00 a.m. - 12:00 p.m.**Textbook:**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 7th edition, 2012

**Content:**Estimation, tests of statistical hypotheses, best tests, sufficient statistics, Rao-Cramer inequality, sequential probability ratio tests, the multivariate normal distribution, nonparametric methods

**Prerequisite:**Grade of C or better in STAT 401**Homework:**Turn in every Wednesday before class; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Midterms:**February 19th (Friday), and April 8th (Friday), 10:00 a.m. - 10:50 a.m.

**Final Exam:**May 6th (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*.

**Course Syllabus**

**WEEK****SECTIONS****BRIEF DESCRIPTION**01/11 - 01/15 4.1; 4.2, 4.4; 4.8 Sampling and Statistics; Confidence Interval, Order Statistics; Method of Monte Carlo 01/18 - 01/22 Holiday; 4.9; 6.1 Bootstrap Procedures; Maximum Likelihood Estimation 01/25 - 01/29 6.1; 6.2; 6.2 Rao-Cramer Lower Bound and Efficiency 02/01 - 02/05 6.3; 6.3; 6.4 Maximum Likelihood Tests; Multiparameter Case: Estimation 02/08 - 02/12 6.4; 7.1; 7.1 Multiparameter Case: Estimation; Measures of Quality of Estimators 02/15 - 02/19 7.1; Review; **Midterm-1**Measures of Quality of Estimators 02/22 - 02/26 7.2; 7.2; 7.3 Sufficient Statistic; Properties of Sufficient Statistic 02/29 - 03/04 7.4; 7.5; 7.5 Completeness and Uniqueness; Exponential Class of Distributions 03/07 - 03/11 7.7; 7.7; 7.8 Case of Several Parameters; Minimal Sufficiency and Ancillary Statistics 03/14 - 03/18 7.8; 7.9; 7.9 Minimal Sufficiency and Ancillary Statistics; Sufficiency, Completeness and Independence 03/28 - 04/01 8.1; 8.1; 8.2 Most Powerful Tests; Uniformly Most Powerful Tests 04/04 - 04/08 8.2; Review; **Midterm-2**Uniformly Most Powerful Tests 04/11 - 04/15 8.2; 8.3; 8.3 Uniformly Most Powerful Tests; Likelihood Ratio Tests 04/18 - 04/22 8.3; 11.2; 11.2 Likelihood Ratio Tests; Bayesian Procedures 04/25 - 04/29 11.2; Review; Review Bayesian Procedures 05/02 - 05/06 **Final Exam**Final Exam

**Handout**- Mathematical Symbols
- Derivatives, Integrals and Series
- Power Series
- Table I: Poisson Distribution
- Table III: Normal Distribution

**Homework**- Homework #1, due 01/20/2016

- Homework #2, due 01/27/2016

- Homework #3, due 02/03/2016

- Homework #4, due 02/10/2016

- Homework #5, due 02/17/2016

- Homework #6, due 03/02/2016

- Homework #7, due 03/09/2016

- Homework #8, due 03/16/2016

- Homework #9, due 04/01/2016

- Homework #10, due 04/06/2016

- Homework #11, due 04/20/2016

- Homework #12, due 04/27/2016

- Homework #1, due 01/20/2016
**Using R**- Download
**R**for Free -- the most popular software used by statisticians

- Learn R in 15 Minutes

- Use R to Compute Numerical Integrals

- RStudio -- a convenient set of integrated tools for R, including programming, plotting, and workspace management

- Downloadable Books on R:
*An Introduction to R*, by William N. Venables, David M. Smith and the R Development Core Team

*Using R for Data Analysis and Graphics - Introduction, Code and Commentary*, by John H. Maindonald

**More R Books in Different Languages ...**

- Download
- R Code for the Course:

- Textbook Web Page -- including Errata page and R code

- Lecture Notes written by Prof. Ryan Martin

- R. A. Fisher and the Making of Maximum Likelihood (for §6.1)

- Interchange of Differentiation and Integration (for §6.2)

- Factorization Theorem for Determining a Sufficient Statistic (for §7.2)

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