Heavy tails and their extremes in space and time: analyzing data for rare events and estimating future risks
Abstract
Heavy tailed models are necessary to adequately explain high variability and lack of symmetry observed everywhere . Heavy tails decay slower than exponentially fast. This sometimes involves infinite variance and even infinite mean. This project will develop a set of mathematical and statistical tools different from those used under Gaussian and other light-tailed scenarios and based on analysis of variance, correlations and moment generating functions. The proposal has 3 interacting themes dealing with heavy tails and their extremes. Theme I: spatial and spatial-temporal extremes . The proposed research will develop flexible spatial and spatial-temporal models as well as prove theorems for point processes based on random fields, for the total observed numbers over large areas and for the maximal observed numbers over large areas. We will also investigate extremes in unobserved locations. Some of the models will be of the fractional type, to reflect the frequently observed natural phenomena. Theme 2: understanding the amount of data needed to guarantee quality of forecasting extremes and designing data-economical procedures . The proposed research will develop mathematical theory needed to understand the minimal data requirements for risk forecasting in crucial in military applications. Based on this theory the proposal will develop statistical techniques for risk forecasting that use the minimal amount of data necessary. Theme 3: working with imperfect extremes . The proposed research will develop new mathematical dealing with missing extremes and the situations where a sharp boundary between extremes and non-extremes is impractical or undesirable. This includes designing estimators that robust with respect to missing extremes md smooth transitions between extremes and non-extremes .
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1810318
Entities
People
- Gennady Samorodnitsky
Organizations
- Army Contracting Command
- Cornell University
- United States Army