An introductory graduate level course. This is the second part of one-year series course in mathematical statistics.
Instructor: Jimin Ding;
Office Hours:
Tue. 2:30-3:30pm. or by appointment. You can also email me your questions.
Topics covered:
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U-statistics; estimation in parametric models, Quasi-likelihoods, MLEs, M-estimators; hypothesis testing, Neyman-Pearson lemma, UMP an UMPU tests, likelihood ratio test, Wald test, score test, confidence sets, pivotal quantity, bootstrap confidence sets.
Prerequisites:
Math 5061 (Theory in Statistics I) is recommended but not required. You should be
familiar with the following (which have been covered in math 5061):
probability space and distributions; characteristic functions; convergence in probability and distribution; law of large numbers, central limit
theorem; delta method; unbiased and sufficient statistics; exponential family. You are welcome to consult with the instructor before the class.
Textbook:
Jun Shao,
Mathematical Statistics, 2nd edition
Springer, 2003, ISBN 0-387-95382-5
Exams:
Midterm: March.05 (Thur).
Final: April. 23 (Thur) in class -- Temporal
Both midterm and final will be in-class closing-books-and-notes exams. You may take no more than 1 page (letter size, double-sided) sheet.
Homeworks:
Homework will be collected every week on other Thursday. No late homework will be accepted.
You may use the known results, which have been shown in the textbook examples or the previous homeworks, in your solutions and proofs with clear references.
Grades:
Grades will be based on the homework sets (around 50%), on the midterm (around 20%) and on the final (around 25%).
Collaboration:
Collaboration on homework is allowed and can be helpful (and fun).
However, you must do all written work by yourself. In class exams have to be finished independently.
Some good references:
Elements of Large-Sample Theory. E.L. Lehmann, Springer, 1999.
Theory of Point Estimation. E.L. Lehmann and G. Casella, Springer, 2005.
Testing Statistical Hypothese. E.L. Lehmann and R.P. Romano, Spinger, 3rd edition, 2008.
Mathematical Statistics. P. Bickel and K.A. Doksum, Prentice Hall, 2nd edition, 2006.