Seminars 2008 — Abstracts

Friday, April 18

Speaker: Nader Tajvidi, Lund Institute of Technology

Title: On Distribution Estimation and Prediction for Bivariate Extreme-Value Distributions

Abstract: Two new methods are suggested for estimating the dependence function of a bivariate extreme-value distribution. One is based on a multiplicative modification of an earlier technique suggested by Pickands, and the other employs spline smoothing under constraints. Both produce estimators that satisfy all the conditions that define a dependence function, including convexity and the restriction that its curve lie within a certain triangular region. The first approach does not require selection of smoothing parameters; the second does, and for that purpose we suggest explicit tuning methods, one of them based on cross-validation. Applications of our dependence function estimators to estimating the full bivariate distribution, and its density, are described, as too are applications to prediction. Indeed, the cross-validation algorithm is designed to provide near-optimal performance when estimating the bivariate density, and is particularly useful for constructing compact prediction regions by the method of profiling.