# STATISTICAL INFERENCE

iten
Code
48384
2021/2022
CREDITS
11 credits during the 2nd year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA

8 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

8 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
SECS-S/01
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Mathematical Statistics and Data Management)
semester
2° Semester
Teaching materials

## OVERVIEW

a) Introduction to Statistical Inference

b) Introduction to sampling theory (only for SMID)

## AIMS AND CONTENT

LEARNING OUTCOMES

a) To provide an introduction to concepts and techniques from statistical inference which are fundamental to provide a probabilistic measure of the error committed when estimation is based on a sample from a large population. b) To deal with theoretical and practical elements of the design, analysis and inference of survey data obtained by probabilistic sampling.

AIMS AND LEARNING OUTCOMES

At the end of the course students will be able:

a)

. to explain the key points defining exploratory data analysis versus statistical inference based on finite samples

. to possess the main concepts and techniques for computing point estimates, confidence intervals and performing hypothesis testing and for evaluating them

. to identify the suitable statistical technique and perform the analysis of simple data sets.

b) only for SMID)

. to judge the validity of a sample survey
. toplan and analyze simple sample surveys also by aid of software
. to evaluate mathematical properties of a probabilistic sample
• to develop further knowledge about the theory and practice of statistical sampling
. to present a report with the analysis of a sample and a critique of its design

PREREQUISITES

a)

Mathematical Analysis: function of a variable, integral calculus.
Algebra: elements of vector and matrix algebra.
Probability: elementary probability

b)(only for SMID)

Statistical Inference part a) in parallel

TEACHING METHODS

a) Combination of traditional lectures (40 hours) and exercises sessions (24 hours)

b) Combination of traditional lectures and lab sessions with the software R(only for SMID)

SYLLABUS/CONTENT

a)

Sampling and estimation. Populations, samples and point estimators. Properties of point estimators. Some point estimators and their probability distributions. Confidence intervals.
Hypothesis tests. How to define and use a statistical test (hypotheses, errors of the first and second type, critical region). Parametric tests. Tests of large samples. Comparative tests. Some non-parametric tests.
Statistics and tests for linear multiple models. Confidence intervals for the parameters, estimated values and residuals, "studentized" residuals, test of hypotheses on single coefficients and on subsets of coefficients. Forecast.

b)(only for  SMID)

Statistical sampling from a finite population. Simple random sampling with and without replacement. Stratified sampling. Proportional allocation and optimal allocation. Statistical estimators of means and their variances.

a)

1. Casella G., Berger R.L. (2002), Statistical Inference, Pacific Grove, CA: Duxbury

2. Mood A.M., Graybill F.A., Boes D.C. (1991), Introduction to the Theory of Statistics, McGraw-Hill, Inc.

3. Ross S.M. (2003), Probabilità e statistica per l’ingegneria e le scienze, Apogeo, Milano

4. Wasserman L. (2005), All of Statistics, Springer

5. Records of the teachers on aula web

b)(only for SMID)

1. Vic Barnett Sample Survey, Principle and methods, Third Edition, John Wiley & Sons, Ltd, 2002

2. William Cochran, Sampling Techniques, John Wiley & Sons,1977

3. Sharon L.Lohr, Sampling: Design and Analysis. Second Edition, Brooks/Cole, 2010

4. Records of the teachers on aula web or http://www.dima.unige.it/ rogantin/StatI/index.htm

## TEACHERS AND EXAM BOARD

Office hours: By appointment arranged by email with Luca Oneto&nbsp;luca.oneto@unige.it&nbsp;and Fabrizio Malfanti &lt;fabrizio.malfanti@intelligrate.it&gt; For organizational issues contact by email Eva Riccomagno &lt;riccomagno@dima.unige.it&gt; &nbsp;

Office hours: Contact the teacher: guala@dima.unige.it &nbsp;

Exam Board

EVA RICCOMAGNO (President)

ELDA GUALA

## LESSONS

TEACHING METHODS

a) Combination of traditional lectures (40 hours) and exercises sessions (24 hours)

b) Combination of traditional lectures and lab sessions with the software R(only for SMID)

LESSONS START

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

a)

The exam consists of a written and a oral part.

During the semester there will be three (not evaluated) mock exams. The lecture after each mock exam will start with a 15-minute closed-book written examination.

The first two closed-book examinations are evaluated at most 3 marks and the third one at most 2 marks, for a maximum total of 8 marks.

For the students who attempted all of the three closed-book examinations, the final written examination consists of a 2-hour open book examination, which is evaluated at most 23 marks to be added to the marks of the three on-course closed-book examinations.

For the students who did not attempt the three closed-book examinations, the final written examination consists of two parts: a 45-minute closed-book examination and a 2-hour open-book examination. The closed-book part is evaluated at most 8 points, the open-book part is evaluated at most 23 points.

b)(only for SMID)

Written exam with multiple choice and open questions. A group project on a topic agreed with the teachers. Discussion of the report and written test.

ASSESSMENT METHODS

a)

The on-course examination and the closed-book part of the final examination test the comprehension of the theory.

The two-hour open-book examination evaluates the acquired ability to apply the theoretical ideas for simple data analysis.

b)(only for SMID) Main points of evaluation are the level of acquisition of the learning objectives and the ability to communicate in a written report the data analyzes carried out during the course as well as the ability of designing a simple sampling scheme, conducting it on a softare, analyse the results and synthesize them in a short report.

Exam schedule

Date Time Location Type Notes
20/01/2022 09:00 GENOVA Scritto + Orale solo per gli studenti che hanno frequentato l'insegnamento nell'a.a.2020/21 o in a.a. precedenti
10/02/2022 09:00 GENOVA Scritto + Orale solo per gli studenti che hanno frequentato l'insegnamento nell'a.a.2020/21 o in a.a. precedenti
27/06/2022 09:00 GENOVA Scritto + Orale
26/07/2022 09:00 GENOVA Scritto + Orale
19/09/2022 09:00 GENOVA Scritto + Orale