Ensimag Rubrique Formation 2022

Advanced inferential statistics - 4MMSIA

  • Number of hours

    • Lectures 16.5
    • Tutorials 16.5

    ECTS

    ECTS 2.5

Goal(s)

This course presents the mathematical theory of statistical inference. It deepens and completes the Statistical Principles and Methods course.

Contact Olivier GAUDOIN

Content(s)

1. Concepts of statistical inference. Statistical model. Likelihood. Sufficiency.
2. Optimal parametric estimation. Minimum variance unbiased estimation. Fisher Information.
3. Properties of the maximum likelihood estimator. Bayesian statistics.
4. Optimal parametric tests. Neyman-Pearson lemma. Uniformly most powerful tests.
5. Nonparametric estimation. Order and rank statistics.
6. Functional estimation.



Prerequisites

Probability Theory and Applications, Statistical Principles and Methods (first year).

Test

Written exam (3 hours, documents allowed) (E).



N1 = E1
N2 = E2

Additional Information

Curriculum->MMIS.->Semester 4
Curriculum->For Financial Engineering->Semester 4

Bibliography

Polycopié de cours.
D. FOURDRINIER : Statistique inférentielle, Dunod, 2002.
M. LEJEUNE : Statistique, la théorie et ses applications, Springer, 2004.
A. MONFORT : Cours de Statistique Mathématique, Economica, 1997.
J.A. RICE : Mathematical Statistics and Data Analysis, Duxbury Press, 1995.
J. SHAO : Mathematical Statistics, Springer, 1998.