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KnowledgeThe student who successfully completes the course will have the ability to understand the mathematical basis of Statistics. He will have a critical knowledge of the main theorems and results related to statistical concepts (test, estimators, confidence intervals and so on). He will also practice with some distribution functions of importance in Statistics. Worked exercises will help him to grasp the theory.
Assessment criteria of knowledge- During the oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression.
- Final oral exam
Delivery: face to face
- attending lectures
- participation in seminar
- preparation of oral/written report
- participation in discussions
- individual study
- Laboratory work
SyllabusStatistical models, estimators, sufficient statistics, Neymann-Fisher Theorem, quadratic loss. Unbiased estimators Blackwell Rao Theorem, Exponential models, Fisher information and its properties, Cramer Rao bound, efficient estimators. Kullback information and its connection with Fisher information. Maximum likelihood estimators and their main asymptotic properties. Gaussian random vectors. Cochran Theorem. Linear models, Gauss-Markov Theorem, confidence regions, statistical tests, Anova, Behrens-Fisher problem, empirical distribution function, Glivenko-Cantelli Theorem, chi square test. Elements of bayesian statistics.
BibliographyNotes of the course will be available. Recommended reading includes: Dacunha-Castelle, D.; M. Duflo: Probability and Statistics I and II, Springer-Verlag Shao, J. : Mathematical Statistics, Springer Texts in Statistics Further bibliography will be indicated during the lectures if necessary.
Ultimo aggiornamento 14/11/2016 17:27