# Course description.

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# Section 1. Course description.

Professor: Antonietta Mira
Assistant: Reza Solgi
Assistant: Stefano Peluso

Course type: Master +2
Value in ECTS: 6
Bibliographic references available on the University Library website

Academic year 2012/2013 - Fall semester

Contents
The course deals with statistical model-building and statistical inference. Although the main focus of the course is theoretical and methodological, the statistical freeware software R will be introduced and used to analyse economical and financial data sets.
The software R is the free version of the commercial software "Splus" (one of the main software used for statistical purposes) and can be downloaded from the website: http://www.r-project.org/.

Prerequisites
The students will be assumed to have learned, in previous classes, the following concepts of probability theory and descriptive statistics.
In the week 19-22 of September there will be a test to check the level of the students knowledge on the pre-requisites so that students in need to refresh their probability background can be advised to sit in the Probability I class.
On the website of the course there are also lecture notes to review the topics mentioned below that are a pre-requisite for the course.

Probability Theory
Introduction to probability: definitions, concept of marginal and joint probability, low of total probability, conditional probability, notion of independence.
Random variables: discrete (Bernoulli, Binomial, Geometric, Poisson, Uniform), continuous (Uniform, Gaussian or Normal, Exponential, Student-T, Chi-square).
Central limit theorem and Law of large numbers.

Descriptive Statistics
Univariate: measure of location (mean, median, mode) and dispersion (variance, std deviation, quantiles).
Bivariate: two way tables, joint and marginal distributions, covariance and correlation.
Graphical instruments to visualize data.

Details of the course
The first week will be spent reviewing the above mentioned requirements and there will be a test to check the level of the students knowledge on the pre-requisites.
The course focuses on inferential statistics:

Main topics
- Advance probability theory: moment generating function; exponential family; multivariate distributions; marginal and conditional distributions; independence; correlation.
- Likelihood concepts. Definition of likelihood function; main properties of likelihood function.
- Parametric estimation; various principles for generating estimators (including maximum likelihood, method of moments, Bayesian estimation) and their properties (finite sample and asymptotic properties).
- Construction of confidence (credible) intervals and sets.
- Theory of hypothesis tests.
- Introduction to nonparametric inference.

Main references
Lecture notes will be available on the e-learning website.
G. Casella and R.L. Berger, Statistical Inference, Pacific Grove, 1990.

Further references
E.L. Lehmann and G. Casella, Theory of point estimation, second edition, Springer, 1998.
E.L. Lehmann, Testing statistical hypotheses, second edition, Springer, 1986.
A.M. Mood, F.A. Graybill, D.C. Boes, Introduction to the theory of statistics, 3. ed. - McGraw-Hill, New York, 1974 (also available in Italian).

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