# STATISTICAL INFERENCE

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

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

OVERVIEW

a) Introduction to Statistical Inference

b) Introduction to sampling theory

## 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:

- to explain the key points defining exploratory data analysis versus statistical inference based on finite samples (part a)
- to possess the main concepts and techniques for computing point estimates, confidence intervals and performing hypothesis testing and for evaluating them (part a)
- to identify the suitable statistical technique and perform the analysis of simple data sets (part a).
- to judge the validity of a sample survey (part b)
- to plan and analyze simple sample surveys also by aid of software (part b)
- to evaluate mathematical properties of a probabilistic sample (part b)
- to develop further knowledge about the theory and practice of statistical sampling (part b)
- to present a report with the analysis of a sample and a critique of its design (part b)

PREREQUISITES

Part a:

*Mathematical Analysis*: function of a variable, integral calculus.

*Algebra*: elements of vector and matrix algebra.

*Probability*: elementary probability

Part b:

Probability and Statistical Inference

Teaching methods

Part a:

Combination of traditionals lectures (40 hours) and exercises sessions (24 hours).

Part b:

Combination of traditionals lectures and lab sessions with the software R (24 hours).

SYLLABUS/CONTENT

*Part a:*

*Estimation.* 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. Large sample tests. 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.

Part b:

Statistical sampling from ea finite polulation. Simple random sampling with and without replacement. Stratified sampling. proportional allocation and optimal allocation. Statistical estimators of means and their variances.

RECOMMENDED READING/BIBLIOGRAPHY

Part a:

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

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

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

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

Handouts on aulaweb

Part b:

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

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

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

Handouts on aulaweb

## TEACHERS AND EXAM BOARD

**Ricevimento:** By appointment arranged by email with guala@dima.unige.it

**Ricevimento:** By appointment arranged by email with Luca Oneto luca.oneto@unige.it and Fabrizio Malfanti <fabrizio.malfanti@intelligrate.it>
For organizational issues contact by email Eva Riccomagno <riccomagno@dima.unige.it>

Exam Board

EVA RICCOMAGNO (President)

ELDA GUALA (President)

EMANUELA SASSO

MARTA NAI RUSCONE

## LESSONS

Teaching methods

Part a:

Combination of traditionals lectures (40 hours) and exercises sessions (24 hours).

Part b:

Combination of traditionals lectures and lab sessions with the software R (24 hours).

LESSONS START

The class will start according to the academic calendar.

## EXAMS

Exam description

Part 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.

Part b:

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

Part 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.

Part b:

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.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

23/06/2020 | 09:00 | GENOVA | Scritto + Orale | |

16/07/2020 | 09:00 | GENOVA | Scritto + Orale | |

09/09/2020 | 09:00 | GENOVA | Scritto + Orale |

## FURTHER INFORMATION