Statistical Theory

Instructor: Prof. Victor Panaretos

Assistant: Dr. David Kraus

News

The midterm exam will be on Wednesday, November 9th, 10.15-12.00 in 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.

Midterm

The midterm exam will be on Wednesday, November 9th, 10.15-12.00 in MA12.

Exercises/Solutions

Each week all the theory exercises should be attempted. One or two exercises will be graded. The exercise(s) to be graded will be announced after the exercise session (in the end of the week) and should be handed in the following week. The solutions (in paper form) will be distributed together with the corrected exercises.