M2MO: Modélisation Aléatoire, Finance et Data Science

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

Courses Core courses Basics of data modeling and statistical inference

Basics of data modeling and statistical inference

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

This course presents basic concepts of statistical inferenceas well as some classical statistical models and methods.


Statistical experiment (identifiabilty, domination, likelihood)
Consistency, methods for constructing consistent estimators(method of moments, method of maximum likelihood)
Empirical distribution function. Glivenko-Cantelli theorem, empirical quantile
Confidence intervals
Hypothesis testing: Neyman-Pearson test, Wald test, Chi-squared tests
Gaussian linear model
Statistical decision theory: risk function, admissibility, minimax estimator
Estimation in the Bayesian formulation
Sufficient statistic, factorization theorem
Regular statistical experiment. The Cramer-Rao inequality
Non-parametric estimation : estimation of an unknown density


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.