28202 - Statistics (A. C.)

Course contents

Fundamentals of probability. Random variables. Expected value, variance and moment-generating function of a random variable. The main probabilistic models. Transforming random variables.

Random vectors. Joint, conditional and marginal distributions. Independence. Sequences of random variables. Limit theorems and convergence. Functions of a random vector. The multivariate normal distribution.

Purposes of statistical inference. Probabilistic models, sampling methods and statistical models. Sampling distributions. Identificability of a statistical model.

The likelihood function and the likelihood principle. Statistics, sufficient statistics and minimal sufficient statistics. Exponential families of distributions.

The problem of point estimation and the solutions obtained by using the maximum likelihood method. Other methods of estimation (outlines). Fisher information and Rao-Cramér inequality. Desirable properties of an estimator and properties of the maximum likelihood estimators.

The hypothesis-testing problem and the solutions obtained according to the Neyman-Pearson approach. The likelihood ratio test and its most important applications.

Introduction to latent variable models. Structural equation LISREL models.

Readings/Bibliography

J. H. McColl, Multivariate probability. Arnold, London, 2004.

A. Azzalini, Inferenza statistica. Una presentazione basata sul concetto di verosimiglianza. 2° edizione, Springer-Verlag Italia, Milano, 2001.

S. Cagnone, Appunti sulla metodologia LISREL: aspetti teorici e applicativi, Dipartimento di Scienze Statistiche "Paolo Fortunati", Università degli studi, Bologna, 2005.

Teaching methods

Theoretical and practical lessons.

Assessment methods

Written and oral exam.

Teaching tools

Some additional readings concerning the topics which are not included in the recommended textbooks will be indicated during the lessons.

Office hours

See the website of Gabriele Soffritti