M2MO: Modélisation Aléatoire, Finance et Data Science

Master en statistique, probabilités et finance - Université Paris 7 - Paris Diderot

Courses Core courses Data modeling and statistical inference

Data modeling and statistical inference

Lectures: S. Delattre
S. Gribkova
Périod: Term 1
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.


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


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.