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 Note 6.pdf
