Lectures:	S. Delattre
Tutorials:	S. Gribkova
Périod:	Term 1
ECTS:	6
Hourly Volume:	3 hours of lectures  and  3 hours of tutorials

Statistical inference is the process of using data to infer the distribution that generated the data. This course presents important concepts as well as some classical statistical models and methods.

Outline:

1) Empirical distribution function. Glivenko-Cantelli theorem, empirical quantile

2) Density estimation : histograms, kernels

3) Consistency, methods for constructing consistent estimators (method of moments, method of maximum likelihood)

4) Hypothesis testing: Neyman-Pearson test, Chi-squared tests, Kolmogorov-Smirnov test

5) Multivariate regression

6) Statistical decision theory: risk function, admissibility, minimax estimator
Estimation and test in the Bayesian formulation

7) Nonparametric regression

Bibliography:

Fetsje Bijma, Marianne Jonker, Aad van der Vaart. An Introduction to Mathematical Statistics, Amsterdam University Press, 2017.

Ibragimov,  Hasʹminskiĭ. Statistical estimation. Asymptotic theory.Applications of Mathematics, 16. Springer-Verlag, New York-Berlin, 1981.

Wasserman. All of statistics. A concise course in statistical inference. Springer Texts in Statistics.Springer-Verlag, New York, 2004.