Modules | Area | Type | Hours | Teacher(s) | |
STATISTICA MATEMATICA | MAT/06 | LEZIONI | 48 |
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Il corso intende dare le basi matematiche della Statistica Inferenziale
The 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.
Esame orale
- 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.
Methods:
Saper gestire le conoscenze acquisite a livello pratico
Esercizi svolti in classe
Il corso di" Probabilita'"
Delivery: face to face
Learning activities:
Attendance: Advised
Teaching methods:
Statistical 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.
l corso si baserà principalmente su appunti (non ancora in forma definitiva), disponibili in rete all'indirizzo
http://people.dm.unipi.it/giuliano/nuovo_sito/dispensestatisticamatematica.pdf
Ottimi testi sono i seguenti: --P. Baldi (1997), Calcolo delle Probabilit\`{a} e Statistica, Mc-Graw Hill Italia, Milano --D. Dachuna-Castelle, M. Duflo (1986) Probability and Statistics, Springer, New York.Notes 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.
Colloquio orale
http://people.dm.unipi.it/giuliano/nuovo_sito/indexstatmat.html