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
Tutorials: 
S. Has
Périod: Term 1
ECTS:
6
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.

Outline:

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

Bibliography:

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.