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## STATISTICAL MODELS

CODE 41601 2021/2022 9 cfu during the 1st year of 11267 ECONOMICS AND DATA SCIENCE (LM-56) - GENOVA SECS-S/01 English GENOVA 2° Semester Prerequisites You can take the exam for this unit if you passed the following exam(s): ECONOMICS AND DATA SCIENCE 11267 (coorte 2021/2022) SOFTWARE R 106839 Prerequisites (for future units) This unit is a prerequisite for: Economics and Financial Institutions 8700 (coorte 2021/2022) FINANCIAL ECONOMETRICS 85554 AULAWEB

## OVERVIEW

The course aims at providing a thorough account of classical and modern statistical inference at an intermediate level. The topics range from classical inference based on likelihood to regression and classification techniques, with an introduction to simulation techniques in Statistics.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course aims to provide a precise overview of statistical inference at an intermediate level. The first part concerns classical mathematical statistics, based on likelihood, with some hints on simulation-based techniques. The second part of the course focuses on the main regression and classification techniques. In particular, generalized linear models for both discrete and continuous responses will be treated. Some non-parametric regression and classification methods will then be illustrated. Finally, classical methods of validation, model selection, and dimensionality reduction will be addressed.

### AIMS AND LEARNING OUTCOMES

The course is divided into two parts:

1) Some topics in classical inferential Statistics: the main families of univariate and multivariate distributions, simulation, theory of statistical models, the likelihood and its properties.

2) Statistical models for classification and regression. Multiple regression, generalized linear model theory, logistic regression and regression for count data, nonparametric techniques. Nonparametric techniques. Model selection techniques.

All the topics will be accompanied by practical exercises in R, so that the student can also combine the understanding of the theory with the ability to apply correct statistical analyses in real contexts and to read correctly the output of the statistical procedures.

Knowledge and understanding: Students will know the main techniques and the main tools for inferential statistics. They must be able to frame these tools in general terms (both theoretical and applied), and to analyze the underlying mathematical and statistical background.

Ability to apply knowledge and understanding: Students will be able to identify, when faced with problems from different contexts, the correct analysis. Moreover, they will be able to evaluate the results obtained through statistical software.

Making judgments: Students will have to become aware of the potential and limits of the statistical techniques, through the analysis of examples and case studies.

Communication skills: Students must be able to use the correct technical statistical language for the communication of the results and for the description of the techniques.

Learning skills: Students will develop adequate learning skills in order to continue with further studies about other aspects of the subject and different fields of application than those illustrated. Furthermore, they must also be able to use the R software in a general context.

### PREREQUISITES

The classical content of the introductory courses in Mathematical and Statistics for Economics and Business.

### TEACHING METHODS

Lectures and computer lab tutorials with R. Discussion of case studies.

### SYLLABUS/CONTENT

0. Introduction and basic recalls on estimation and hypothesis testing.

1. Some families of discrete and continuous probability distributions.

2. Multivariate distributions.

3. Simulation. Distribution-based simulation and agent-based simulation.

4. Likelihood and sufficiency. Maximum likelihood estimation. Information. The exponential family.

5. Multiple linear regression and k-NN techniques.

6. Generalized linear models theory.

7. Logistic regression and regression for count data.

8. Model selection and regularization.

Evans, Rosenthal, Probability and Statistics. The Science of Uncertainty, Second edition.

James G, Witten D, Hastie T and Tibshirani R, An Introduction to Statistical Learning. With Applications in R. Springer (available from the Authors’ webpage).

Further readings will be taken from:

Casella G and Berger RL, Statistical Inference. Duxbury

Efron B and Hastie T, Computer Age Statistical Inference. Algorithms, Evidence, and Data Science. Stanford University (available from the Authors’ webpage).

Additional course materials (both in Italian and in English) will be available on AulaWeb.

## TEACHERS AND EXAM BOARD

### Exam Board

FABIO RAPALLO (President)

MARTA NAI RUSCONE

## LESSONS

### LESSONS START

This class follows the Department calendar for the 2nd semester.

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

Due to the COVID outbreak, if the on-site exams will be allowed, the exam will be a Written exam. There will be two intermediate exams – only for student who attend the lectures on a regular basis – which replace the final exam.

If there will be the need of on-line exams, we try to keep the exam in written form with upload of the answer sheets. Students will be informed as soon as possible of any change.

The complete exam rules will be available on the class Aulaweb page, and updated when necessary on the basis of the Covid rules.

### ASSESSMENT METHODS

The written exam consists of three parts:

1) a general essay question

2) one or more questions on specific topics

3) a comment on a R output.

As far as possible, the questions are chosen in order to cover all the topics of the course. The general question aims at assessing the degree of knowledge of the subject and the acquisition of the correct technical language, the specific questions are aimed at assessing the critical ability of the student, while the purpose of the comment to the output is to evaluate the application capabilities.

### Exam schedule

Date Time Location Type Notes
17/01/2022 09:30 GENOVA Scritto
07/02/2022 09:30 GENOVA Scritto
04/05/2022 14:00 GENOVA Scritto appello straordinario riservato esclusivamente ai laureandi a.a. 2020/21
06/06/2022 15:00 GENOVA Scritto
20/06/2022 15:00 GENOVA Scritto
12/07/2022 15:00 GENOVA Scritto
06/09/2022 15:00 GENOVA Scritto