Objectives

In this curricular unit some fundamental concepts of probability theory are studied, namely random variables, their properties and functions. Fundamental concepts and methods of statistics are discussed. We also study underlying methods and models used in the statistical analysis of extreme values.

Program

1. Random variables, distribution functions and moments-generating functions
2. Estimators, confidence intervals, and hypothesis tests
3. Multiple Linear Regression
4. Extreme Value Theory
5. Machine learning
6. Linear classifiers
7. Neural networks

Bibliography

• Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J., De Waal, D., and Ferro, C. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability and Statistics.
• Casella, G. and Berger, R. (2002). Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury.
• Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling extremal events: for insurance and finance, Springer.
• Griffiths, W., Hill, R., and Judge G.,  Learning and Practing Econometrics, John Wiley & Sons, 1993
• Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2a edição. McGraw-Hill
• Wooldridge, J. – Introductory Econometrics: A Modern Approach, South-Western College Publishing, 2000