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# Chair of Mathematical Statistics (SMAT)

# Statistical Theory - MATH 442

#### Instructor: Dr. Guillaume Dehaene

#### Assistant: Tomáš Rubín

#### Annoucments

- The exercise session on October 9 is cancelled due to the cancellation of the previous lecture. The lecture on October 9, 10:15-12:00, is taking place according to schedule. From the following week onwards, i.e. October 16, both the exercise session and the lecture take place as usual.

#### Description

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.

#### Topics include:

- 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.

#### Recommended Texts

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.

#### Exam Information

There will be a written final exam.

__No notes, books or any other material will be allowed in the exams.__

#### Exercises/Solutions

Every week, one exercise will be graded. The solutions will be provided in the exercise session following the submission of the exercises. The grades from homeworks are for feedback only and will not count towards the final grade.

#### Fall 2018 Schedule

Lectures: | MA A1 12 | Tuesdays, 10:15-12:00 |
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Exercises: | MA A1 12 | Tuesdays, 8:15-10:00 |