Statistical theory
Summary
This course gives a mostly rigourous treatment of some statistical methods outside the context of standard likelihood theory.
Content
Review of decision and likelihood theory in parametric models. Shrinkage and superefficient estimators. Adaptive estimation. kNN classification. Optimal transport and application to the bootstrap. If time permits, M-estimation.
Keywords
Nonparametrics, inference, optimal transport, classification, shrinkage
Learning Prerequisites
Required courses
Courses on basic probability and statistics (e.g., MATH-240, MATH-230)
Recommended courses
Probability theory (MATH-432), Measures and integration (MATH-303)
Important concepts to start the course
Nothing specific is strictly necessary, but the pace will assume some level of mathematical and statistical maturity.
Learning Outcomes
- Formulate the various elements of a statistical problem rigorously.
- Formalize the performance of statistical procedures through probability theory.
- Systematize broad classes of probability models and their structural relation to inference.
- Construct efficient statistical procedures for point/interval estimation and testing in classical contexts.
- Derive certain exact (finite sample) properties of fundamental statistical procedures.
- Derive certain asymptotic (large sample) properties of fundamental statistical procedures.
- Formulate fundamental limitations and uncertainty principles of statistical theory.
- Prove certain fundamental structural and optimality theorems of statistics.
Expected student activities
Attending and actively interacting during lectures.
Assessment methods
Final written exam.
Supervision
Office hours | No |
Assistants | Yes |
Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Notes/Handbook
There will be lecture notes.
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Statistical theory
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
Reference week
Mo | Tu | We | Th | Fr | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Lecture
Exercise, TP
Project, Lab, other