# 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.

## 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