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.

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