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Activity Number: 602
Type: Contributed
Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #312214
Title: On All of the Possible Extensions of a Two-Dimensional Semi-Copula to a Copula
Author(s): Francois Perron*+
Companies: Universite de Montreal
Keywords: copula ; semi-copula ; sigma algebra ; cantor set ; semi algebra ; extension
Abstract:

A semi-copula D is the restriction of a Copula C_0 on a product space R_1 x R_2, R_1, R_2 are any subset of [0,1], they contain 0 and 1. We find all of the copulas C such that the restriction of C on R_1 x R_2 is equal to D. These copulas C are called the extensions of D. We provide a very simple expression for the maximal copula extending D. Our results are very general, we do not assume any condition on R_1 and R_2. In particular, we show that some of the previous attempts are less general because they require conditions on R_1 and R_2.


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