**Course Announcement**

**Time:**Monday, Wednesday, Friday at 9:00 - 9:50 a.m.

**Location:**Lincoln Hall 312**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 10:00 a.m. - 11:00 a.m.**Textbook:**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 8th edition, 2019

**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:**October 4th (Friday), and November 15th (Friday), 9:00 a.m. - 9:50 a.m.

**Final Exam:**(pending...)

**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**08/26 - 08/30 4.1; 4.2, 4.4; 4.8 Sampling and Statistics; Confidence Interval, Order Statistics; Method of Monte Carlo 09/02 - 09/06 Holiday; 4.9; 6.1 Bootstrap Procedures; Maximum Likelihood Estimation 09/09 - 09/13 6.1; 6.2; 6.2 Maximum Likelihood Estimation; Rao-Cramer Lower Bound and Efficiency 09/16 - 09/20 6.3; 6.3; 6.4 Maximum Likelihood Tests; Multiparameter Case: Estimation 09/23 - 09/27 6.4; 7.1; 7.1 Multiparameter Case: Estimation; Measures of Quality of Estimators 09/30 - 10/04 7.1; Review; **Midterm-1**Measures of Quality of Estimators 10/07 - 10/11 7.2; 7.2; 7.3 A Sufficient Statistic for a Parameter; Properties of a Sufficient Statistic 10/14 - 10/18 7.4; 7.5; 7.5 Completeness and Uniqueness; The Exponential Class of Distributions 10/21 - 10/25 7.7; 7.7; 7.8 The Case of Several Parameters; Minimal Sufficiency and Ancillary Statistics 10/28 - 11/01 7.8; 7.9; 7.9 Minimal Sufficiency and Ancillary Statistics; Sufficiency, Completeness and Independence 11/04 - 11/08 8.1; 8.1; 8.2 Most Powerful Tests; Uniformly Most Powerful Tests 11/11 - 11/15 8.2; Review; **Midterm-2**Uniformly Most Powerful Tests 11/18 - 11/22 8.2; 8.3; Holiday Uniformly Most Powerful Tests; Likelihood Ratio Tests 11/25 - 11/29 8.3; 11.1; 11.1 Likelihood Ratio Tests; Bayesian Procedures 12/02 - 12/06 11.1; Review; Review Bayesian Procedures 12/09 - 12/13 **Final Exam**Final Exam

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

**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

- 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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