UNIVERSITY OF JORDAN

Faculty of Science                                                                Department of Mathematics
Mathematical Statistics MATH 931
Spring 2019 /2020

Instructor:     Prof.  Mohammad Al-Raqab
Office Hours: Sunday, Tuesday, 1:00 – 2:00 p.m. or by appointments.

Recommended References:

- Theory of Point Estimation, by E. L. Lehman and G. Casella, 1998, 2nd Edition, Springer.
- Testing of Statistical Hypotheses, by E. L. Lehman and J. P. Romano, 2005, 3rd 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%

Lecture Notes