# 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

Introduction to Statistical Inference

## AIMS AND CONTENT

LEARNING OUTCOMES

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.

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
- possess the main concepts and techniques for computing point estimates, confidence intervals and performing hypothesis testing and for evaluating them
- identify the suitable statistical technique and perform the analysis of simple data sets.

Teaching methods

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

SYLLABUS/CONTENT

*Sampling and estimation. *Populations, samples and point estimators. Properties of point estimators. Some point estimators and their probability distributions. Confidence intervals. Hypothesis tests.

*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.

RECOMMENDED READING/BIBLIOGRAPHY

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

## TEACHERS AND EXAM BOARD

**Ricevimento:** The class will start according to the academic calendar.

**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

ELDA GUALA (President)

EVA RICCOMAGNO (President)

EMANUELA SASSO

## LESSONS

Teaching methods

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

LESSONS START

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## EXAMS

Exam description

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.

Assessment methods

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.

## FURTHER INFORMATION

**Prerequisite**:

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

*Algebra*: elements of vector and matrix algebra.

*Probability*: elementary probability