Extreme Value Theory: Applications and Estimation

Description

This lecture covers the application of Extreme Value Theory in statistical analysis, focusing on extremal limit theorems, point processes, Gaussian processes, Poisson processes, and multivariate extremes. The instructor discusses the theory and applications of extremes in time series, emphasizing the statistical analysis for extremes. Various estimation strategies, such as return level estimation and declustering, are explored, along with the importance of estimating the extremal index. The lecture also delves into modelling strategies using exceedances and the Generalized Pareto Distribution, highlighting the consequences of clustering in stationary series. The instructor demonstrates the estimation of extremal properties and return levels using empirical methods and bootstrap techniques.

Official source

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Generalized extreme value distribution

In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables.

Extremal graph theory

Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure.

Beta prime distribution

In probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind) is an absolutely continuous probability distribution. If has a beta distribution, then the odds has a beta prime distribution. Beta prime distribution is defined for with two parameters α and β, having the probability density function: where B is the Beta function. The cumulative distribution function is where I is the regularized incomplete beta function.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Stone Age

The Stone Age was a broad prehistoric period during which stone was widely used to make stone tools with an edge, a point, or a percussion surface. The period lasted for roughly 3.4 million years and ended between 4,000 BC and 2,000 BC, with the advent of metalworking. Though some simple metalworking of malleable metals, particularly the use of gold and copper for purposes of ornamentation, was known in the Stone Age, it is the melting and smelting of copper that marks the end of the Stone Age.