
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 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
SECSS/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
Examination board not defined
Prerequisites:

Calculus
Linear algebra
Introduction to Probability
Statistics I 
Target skills and knowledge:

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:

Written exam, with theoretical questions and exercises. 
Assessment criteria:

The student is expected to learn concepts, instruments and methodology for an appropriate application of the inferential techniques. 
Course unit contents:

 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, pvalue, 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 loglikelihood ratio and asymptotically equivalents. Onesided version of the loglikelihood ratio test.
 Relevant applications. 
Planned learning activities and teaching methods:

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:

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) 

Pace, L., Salvan, A., Introduzione alla Statistica: II Inferenza, verosimiglianza, modelli. : Cedam, Padova, 2001.

Azzalini, A., Inferenza statistica, una presentazione basata sul concetto di verosimiglianza. : Springer Verlag, 2001.

Cicchitelli, G., Statistica: principi e metodi. : Pearson, 2012.

Piccolo, D., Statistica per le decisioni. : Il Mulino, 2010.


