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Course unit
STATISTICS 2 (Ult. numero di matricola dispari)
SCP4063587, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type |
Scientific-Disciplinary Sector |
Credits allocated |
Basic courses |
SECS-S/01 |
Statistics |
12.0 |
Course unit organization
Period |
First semester |
Year |
2nd Year |
Teaching method |
frontal |
Type of hours |
Credits |
Teaching hours |
Hours of Individual study |
Shifts |
Practice |
2.0 |
28 |
22.0 |
2 |
Lecture |
10.0 |
80 |
170.0 |
No turn |
Examination board
Board |
From |
To |
Members of the board |
8 Commissione a.a.2019/20 (matr.pari) |
01/10/2019 |
30/09/2020 |
MENARDI
GIOVANNA
(Presidente)
ADIMARI
GIANFRANCO
(Membro Effettivo)
FERRACCIOLI
FEDERICO
(Membro Effettivo)
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7 Commissione a.a.2019/20 (matr.dispari) |
01/10/2019 |
30/09/2020 |
ADIMARI
GIANFRANCO
(Presidente)
DALLA VALLE
ALESSANDRA
(Membro Effettivo)
MENARDI
GIOVANNA
(Membro Effettivo)
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6 Commissione a.a 2018/19 (matr.pari) |
01/10/2018 |
31/10/2019 |
MENARDI
GIOVANNA
(Presidente)
ADIMARI
GIANFRANCO
(Membro Effettivo)
VENTURA
LAURA
(Membro Effettivo)
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Prerequisites:
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Calculus
Linear algebra
Introduction to Probability
Statistics I |
Target skills and knowledge:
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The course is intended to provide instruments for inferential data analysis.
Some statistical models and the main inferential methods are illustrated. The course supplies basic information for likelihood inference, as a general framework for data analysis. |
Examination methods:
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Written exam, with theoretical questions and exercises. |
Assessment criteria:
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The student is expected to learn concepts, instruments and methodology for an appropriate application of the inferential techniques. |
Course unit contents:
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- Introduction to Statistical Inference.
- Population, sample, sample data and inference. Statistical models and parametric statistical models.
Empirical control of the statistical model. Empirical distribution function.
- Main parametric statistical models.
- Discrete statistical models: binomial, negative binomial, multinomial, Poisson.
- Continuous statistical models: exponential, gamma, normal and related models.
- Inferential procedures.
- Point estimation. Parameter, estimate, estimator. Method of moments estimator, least squares estimator. Bias, efficiency and consistency of an estimator.
- Confidence intervals and confidence regions. Exact and approximated confidence intervals and confidence regions.
- Hypothesis test. Statistical test, significance level, p-value, power. Exact and approximated tests.
- Likelihood based inference.
- Likelihood function and maximum likelihood estimators (mle).
- Maximum likelihood estimation: computational aspects. Observed and expected information.
Properties of mle's. Approximate distribution of mle: theory, notable examples, applications. Reparameterizations.
- Tests and confidence regions based on mle. Tests and confidence regions based on the log-likelihood ratio and asymptotically equivalents. One-sided version of the log-likelihood ratio test.
- Relevant applications. |
Planned learning activities and teaching methods:
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The course is organized in lectures and exercise group sessions (two groups). Exercise sessions assume an an active involvment of the students. |
Additional notes about suggested reading:
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The first two references below represent the main material for study.
Students can deepen their knowledge with the further references provided.
Further possible material will be provided during the classes on the Moodle. |
Textbooks (and optional supplementary readings) |
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Pace, L., Salvan, A., Introduzione alla Statistica: II Inferenza, verosimiglianza, modelli. --: Cedam, Padova, 2001.
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Azzalini, A., Inferenza statistica, una presentazione basata sul concetto di verosimiglianza. --: Springer Verlag, 2001.
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Cicchitelli, G., Statistica: principi e metodi. --: Pearson, 2012.
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Piccolo, D., Statistica per le decisioni. --: Il Mulino, 2010.
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