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Activity Number: 181
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #319339 View Presentation
Title: Tail Nonexchangeability
Author(s): Paramahansa Pramanik* and Lei Hua and Alan M. Polansky
Companies: Northern Illinois University and Northern Illinois University and Northern Illinois University
Keywords: conditional expectation ; copula ; tail dependence ; tail behavior
Abstract:

The study is about identifying existence of non-exchangeability in the joint distributional tails, and how to quantify the degree of such tail non-exchangeability. The approaches proposed benefit bivariate dependence modeling when tail dependence patterns are important. We propose to use conditional expectations as the basis quantities. Then for random variables X and Y, the departure between tail behavior of E[X|Y> t] and E[Y|X> t], or E[X|Y= t] and E[Y|X= t], becomes sensible in detecting tail non-exchangeability. We use a bivariate copula to model dependency between X and Y. Various devices of generating non-exchangeable copulas as well as three major tail behaviors for univariate margins are studied for the interaction between the departure of those conditional expectations and the non-exchangeable dependence together with various types of margins. Based on the probabilistic properties of the tail non-exchangeability structures, we develop graphical approaches and statistical tests for analyzing dataset that may have non-exchangeability in the joint tail. Simulation study and empirical study are then conducted to demonstrate the usefulness of the proposed approaches.


Authors who are presenting talks have a * after their name.

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