STATISTICAL THEORY (Winter 2009)

Instructor: Prof. Victor Panaretos
Assistant: Dr. David Kraus

Schedule

Lectures: Wednesdays, 10:15-12:00, MA12

Exercises: Wednesdays, 8:15-10:00, MA12

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.

 

For more details see the DETAILED COURSE PLAN

 

Required prior knowledge

The second-year course in statistics; calculus; a first-year course in analysis

 

 

Course Text

Knight, K. (2000). Mathematical Statistics. Chapman and Hall.

 

Exam Information

There will be a written midterm and a written final exam.

No notes, books or any other material will be allowed in the exam.

 

Lecture Slides

 

Week 1 + Week 1 Supplement

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Week 9

Week 10

Week 11

Week 12

Week 13

Week 14

 

Exercises/Solutions

Each week all the theory exercises should be attempted and handed in the following week. One of these exercises will be graded S (satisfactory) or N (not satisfactory).

 

Exercises	Solutions
Exercise Set 1	Solutions 1
Exercise Set 2	Solutions 2
Exercise Set 3	Solutions 3
Exercise Set 4	Solutions 4
Exercise Set 5	Solutions 5
Exercise Set 6	Solutions 6
Exercise Set 7	Solutions 7
Exercise Set 8	Solutions 8
Exercise Set 9	Solutions 9
Exercise Set 10	Solutions 10
Exercise Set 11	Solutions 11
Exercise Set 12	Solutions 12
Exercise Set 13	Solutions 13