Teacher(s)
Language
English
Prerequisites
Concepts and tools equivalent to those taught in teaching units
| LSTAT2190 | Concepts et traitement de vecteurs aléatoires |
| LSTAT2040 | Inférence statistique et vraisemblance |
Main themes
The course is a follow-up to the course LSTAT2040. Concepts in statistical methodology, in particular for optimal inference, will be treated in greater depth and will be complemented by a non-asymptotic theory.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | By the end of the course, the student will have become familiar with the necessary concepts in mathematical statistics complementary to (asymptotic) likelihood theory. The concept of sufficiency has become also important recently for dimension reduction in high-dimensional statistics. The student will be able to put the different themes in a general, abstract context, both regarding their application to problems in statistical analysis and regarding their interpretation. The student will master the technical tools to apply the concepts correctly and will be able to reproduce and to elaborate upon the mathematical arguments underlying the results. The concept of sufficiency has become also important recently for dimension reduction in high-dimensional statistics. |
Content
Theory of Optimality for Statistical Inference
The concept of sufficiency, in particular when applied to the important and rich class of exponential families, delivers a non-asymptotic theory of optimality of statistical procedures. The applications are numerous: for risk-optimal point estimation one can define the concept of UMV(U) estimators, i.e. "uniformly minimal variance (unbiased)" estimators. For the theory of statistical hypothesis testing, to be more abstractly formalised following the Neyman principle, it is possible to characterise the optimality of existing tests via the concept of UMP(U) tests, i.e., "uniformly most powerful (unbiased)" tests. A particular challenge here is the treatment of multi parameter families. Finally, the results from test theory can be directly transferred to define optimality of confidence regions.
The concept of sufficiency, in particular when applied to the important and rich class of exponential families, delivers a non-asymptotic theory of optimality of statistical procedures. The applications are numerous: for risk-optimal point estimation one can define the concept of UMV(U) estimators, i.e. "uniformly minimal variance (unbiased)" estimators. For the theory of statistical hypothesis testing, to be more abstractly formalised following the Neyman principle, it is possible to characterise the optimality of existing tests via the concept of UMP(U) tests, i.e., "uniformly most powerful (unbiased)" tests. A particular challenge here is the treatment of multi parameter families. Finally, the results from test theory can be directly transferred to define optimality of confidence regions.
Teaching methods
The course consists of both lectures and tutorials. The lecture part of the course will often be taught by the concept of "classe inversée", i.e. students read the course material (detailed syllabus) in advance, meet the teacher to prepare a presentation and present the material in front of their peers.
Evaluation methods
There will be an oral exam, preceded by a written preparation. Alternatively, the student will be evaluated on his presentation during the course.
Other information
The course notes will be distributed during the lectures itself. There will also be a Syllabus.
Online resources
https://moodle.uclouvain.be/course/view.php?id=4279
Bibliography
A part du syllabus du cours, les ouvrages suivants sont à conseiller:
- Casella, G., Berger, R.L. (2001). Statistical Inference (2nd ed). Cengage Learning.
- Lehmann, E.L. (1999). Elements of Large-Sample Theory. Springer.
- Lehmann, E.L., Romano, J. (2005). Testing Statistical Hypotheses (3rd ed). Springer.
- Monfort, A. (1997). Cours de statistique mathématique (3rd ed). Economica.
- Casella, G., Berger, R.L. (2001). Statistical Inference (2nd ed). Cengage Learning.
- Lehmann, E.L. (1999). Elements of Large-Sample Theory. Springer.
- Lehmann, E.L., Romano, J. (2005). Testing Statistical Hypotheses (3rd ed). Springer.
- Monfort, A. (1997). Cours de statistique mathématique (3rd ed). Economica.
Teaching materials
- syllabus sur moodle
- copies des slides résumant la matière
Faculty or entity
