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STAT-F404

2021-2022

### Course teacher(s)

Thomas VERDEBOUT (Coordinator) and Gilles NISOL

5

english

## Course content

The course is taught by Prof. Nisol in 2021-2022. Lectures are given in English so the description of the course (even in th French part) is done in English.

Part I (estimation): Conditional expectation/probability, sufficiency, Halmos-Savage theorem, the factorization criterion, minimal sufficiency. Rao-Blackwell theorem, distribution-freeness and ancillarity. Completeness and the Lehmann Scheffé theorem, U-statistics. Exponential families, group equivariance.

Part II (Hypothesis testing): Uniformly most powerfull test, Neyman-Pearson Lemma, Unbiasedness, similarity, Neyman alpha-structure and invariant tests.

## Objectives (and/or specific learning outcomes)

The course is a general course in Mathematical Statistics that will help the student to tackle statistical problems of many different natures. The results of the course do apply in many diferent topics in statistics such as data analysis, multivariate analysis and regression.

The main objective of the course is to provide methods that allow to take optimal decisions (in estimation or hypothesis testing). We describe different statistical principles and properties and show the optimal solutions exist in certain situations.

At the end of the course, the student will have a critical look at what a statistical problem is and its mathematical foundations.

## Prerequisites

### Required knowledge and skills

To follow this course, you need to have a background in Mathematical Statistics already (typically form an introductory course in Mathematical Statistics like Mathematical Statistics I at ULB).

## Teaching methods and learning activities

The course mainly consists in theoretical lecture. We also use active methods to help the student to understand the course.

### Contribution to the teaching profile

Please see the French part (the teaching profile in in French).

### References, bibliography, and recommended reading

Lehmann, E. L., & Casella, G. (1998). Theory of point estimation (Vol. 31). Springer Science & Business Media.

Lehmann, E. L., & Romano, J. P. (2006). Testing statistical hypotheses. Springer Science & Business Media.

## Other information

### Contacts

Université  Libre de Bruxelles (Campus Plaine).

Email: thomas.verdebout@ulb.be

Plaine

## Evaluation

### Method(s) of evaluation

• Other
• Oral presentation
• Project

• english