# Mathematical Statistics CI/SFA

#### KORBA Anna

Department: Statistics

### Objective

The aim of this course is to give the fundamental results in asymptotic statistics on the maximum likelihood estimator and on tests.

At the end of this course, students should be able to

•     Model a statistical problem
•     Calculate likelihood and a maximum likelihood estimator
•     To give the asymptotic behaviour of these estimators
•     Construct tests and interpret their decisions
•     Give the level and power of a test.

### Planning

1) Sampling and Fundamental Theorem of Statistics
2) Plug-in estimators, Delta method, Empirical quantiles
3) Z and M estimators and EMVs
4) Asymptotics of Z and M estimators and Fisher information
5) Comparison of estimators and Cramer-Rao bounds
6) Introduction to testing - Neyman-Pearson's lemma
7) UPP test and monotonous likelihood ratio family
8) Estimation and regression testing
9) Bayesian Statistics

### References

V. Rivoirard et G. Stoltz, "Statistiques en action"
P.J. Bickel et K. Doksum, "Mathematical statistics"
A. Montfort, "Cours de statistique mathématique"
J.J. Daudin, S. Robin et C. Vuillet, "Statistique inférentielle. Idées, démarches, exemples"
D. Fourdrinier, "Statistiques inférentielle : cours et exercices corrigés"
B. Cadre et C. Vial, "Statistique Mathématique Cours et Exercices corrigés"

L. Wasserman, "All of Statistics: A Concise Course in Statistical Inference"