Estatística de Extremos e Aplicações

Objectives

The CU intends to yield advanced statistical theory and most common models in modern Extreme Value Theory (EVT), along with its applications. The students should understand the fundamental concepts of Block Maxima and Peaks-Over- Threshold under maximum domain of attraction (semi-parametric) conditions. They should understand the most important estimators and related properties from both theoretical and practical viewpoints. They should know extensions to modelling extremes in time series (dependence over time), multivariate data and processes (e.g. spatial dependency). The students should learn the most common exploratory statistical tools in order to identify and estimate related quantities to extreme events such as failure probability, value-at-risk and return values emerging in applied areas like environmental sciences, telecommunications, risk analysis and fatigue material. The students should also get in contact with current research topics.

Syllabus

1. Order Statistics. 2.Univariate EVT: maximum domain of attraction, extreme value index; Generalized Extreme Value distribution and Block Maxima method, Generalized Pareto distribution and Peaks-Over-Threshold method; regular variation. 3. Main estimation methods for the extreme value index (Hill, MLE, PWM), high quantiles and tail probabilities: theory and applications. 4. Multivariate extremes, tail dependence and asymptotic independence. Applications. 5. Applications of point processes, time series and methods from spatial statistics in studying extreme events. 6. Advanced subjects shall be referred throughout so that students get in contact with current research topics.

Prerequisites

Approval in: Differential and Integral Calculus, Probability and Statistics.

Cross Competence Component

Critical and innovative thinking: - The realization of exercises and the participation in the classes will develop the strategical and critical thinking, as well as, creativity. - The project realization involves components of strategic thinking, critical thinking, creativity, and problem- solving strategies. Intrapersonal Competencies - The project realization involves components of productivity and time management, stress management, proactivity and initiative, intrinsic motivation and decision making. Interpersonal Skills - The rating of the project report takes into account the form of the reports, the quality of the oral presentation and discussion of the project.

Ethical Principles

All members of a group are responsible for the group’s work In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.