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This course presents the mathematical theory of statistical inference. It deepens and completes the Statistical Principles and Methods course.
Contact Olivier GAUDOIN1. Concepts of statistical inference. Statistical model. Likelihood. Sufficiency.
2. Optimal parametric estimation. Minimum variance unbiased estimation. Fisher Information.
3. Properties of the maximum likelihood estimator. Bayesian statistics.
4. Optimal parametric tests. Neyman-Pearson lemma. Uniformly most powerful tests.
5. Nonparametric estimation. Order and rank statistics.
6. Functional estimation.
Probability Theory and Applications, Statistical Principles and Methods (first year).
Written exam (3 hours, documents allowed) (E).
N1 = E1
N2 = E2
Polycopié de cours.
D. FOURDRINIER : Statistique inférentielle, Dunod, 2002.
M. LEJEUNE : Statistique, la théorie et ses applications, Springer, 2004.
A. MONFORT : Cours de Statistique Mathématique, Economica, 1997.
J.A. RICE : Mathematical Statistics and Data Analysis, Duxbury Press, 1995.
J. SHAO : Mathematical Statistics, Springer, 1998.
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