| Lectures: | S. Delattre |
| Tutorials: |
S. Gribkova |
| 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.
