**UNIVERSITY OF JORDAN **

**Faculty of Science****Department of Mathematics**

**Mathematical Statistics MATH 931**

**Spring 2019 /2020**

**Office Hours**

**:**

**Sunday, Tuesday, 1:00 – 2:00 p.m. or by appointments.**

**Recommended References:**

**- T**

**heory of Point Estimation, by E. L. Lehman and G. Casella, 1998, 2**

^{nd}

**Edition, Springer.**

**- Testing of Statistical Hypotheses, by E. L. Lehman and J. P. Romano, 2005, 3**

^{rd}

**Edition, Springer.**

**- Theoretical Statistics: Topics for a Core Course, by R. Keener, 2010, Springer.**

**Prerequisite:**

**MATH 333: “Probability Theory" and “Math 431: Mathematical Statistics”.**

**Description:**

**This course is aimed at giving the students a thorough understanding of advance statistical inferences including points estimation and hypotheses testing. It includes methods of estimation, some statistical models, asymptotic theory, hypotheses testing.**

**Course Outline**

**:****1– Point Estimation: Probability measures, exponential families, sufficiency, minimal sufficiency, completeness, unbiasedness, Rao-Black Theorem, equivariance estimation, Pitman estimator, Stein estimation (4 weeks).**

**2-**

**Bayesian Inference: Bayesian models, utility theory, minimax estimation, admissibility, Gibbs sampler (2 weeks).**

**3- Hypotheses Testing: Neyman-Pearson Lemma, Uniformly most powerful (UMP) tests, randomized test, confidence region, least favorable distribution, unbiased tests, UMPU: exponential family, invariance, composite hypotheses (3 weeks).**

**4- Large Sample Theory: Information inequality, asymptotic efficiency, maximum likelihood estimation(MLE), asymptotic distribution for the MLE, EM-algorithm, multi-parameter case (2 weeks).**

**5- Large Sample Theory for Likelihood Ratio Tests: Generalized likelihood ratio tests, asymptotic distribution for 2 log**

**, (2 weeks).**

**6- Bootstrap Methods: Bias reduction, parametric bootstrap confidence intervals, (1 week).**

**7- Sequential Methods: Fixed width confidence intervals, stopping times, optimal stopping, sequential probability ratio test, (1 weeks).**

**Grading:Grading:**

**The course grade will be based on your performance in a midterm exam, a final exam and homework assignments as follows:**

**-**

**First Midterm (in class, Tues., Mar. 5, 2019)**

**30%**

**-**

**Second Midterm (in class, Tues., April 23, 2019)**

**30%**

**-**

**Final Exam (in class, will be announced later)**

**40%**