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Statistical Theory - MATH 442
Instructor: Prof. Victor Panaretos
Assistant: Tomáš Rubín
- Exercise for homework from Set 12: Exercise 4 - to be handed in by e-mail either as a PDF file or as a readable photo.
- There will be no exercise session for the Set 13. If you have any problems you can discuss with me (=Tomas) the exercises during my office hours in January.
- Your graded homework from Set 11 (as well as all the other HW that have not yet been collected) you can find in the box next to my office.
- I (=Tomas) offer you office hours on January 16th, 17th, and 18th. Feel free to come to my office anytime but it will be better to write me a short e-mail (email@example.com) in advance.
The course aims to develop certain key aspects of the theory of statistics, providing a common general framework for statistical methodology. While the main emphasis will be on the mathematical aspects of statistics, an effort will be made to balance rigor and relevance to statistical practice.
- Stochastic convergence and its use in statistics: modes of convergence, weak law of large numbers, central limit theorem.
- Formalization of a statistical problem : parameters, models, parametrizations, sufficiency, ancillarity, completeness.
- Point estimation: methods of estimation, the plug-in principle, influence curves, relative efficiency.
- Likelihood theory: the likelihood principle, asymptotic properties, misspecification of models, the Bayesian perspective.
- Optimality: decision theory, minimum variance unbiased estimation, Cramér-Rao lower bound, efficiency.
- Testing and Confidence Regions: Neyman-Pearson setup, likelihood ratio tests, UMP tests, duality with confidence intervals, confidence regions, large sample theory, goodness-of-fit testing.
Required prior knowledge
The second-year courses in probability and statistics; calculus; a first-year course in analysis.
Bickel. P.J. & Doksum, K.A. (2000). Mathematical Statistics: Basic Ideas and Selected Topics, Volume I. Prentice Hall.
Knight, K. (2000). Mathematical Statistics. Chapman and Hall.
Cox, D.R. & Hinkley, D.V. (1979). Theoretical Statistics. Chapman & Hall.
There will be a mock midterm exam (test blanc) and a written final exam.
No notes, books or any other material will be allowed in the exams.
There was mid-term exam (mock exam) on November 16, 9:30 - 11:30 in MA12.
Every week, one or two exercises will be graded to provide feedback. The solutions will be provided in the exercise session following the submission of the exercises.