Regular Vines: Generation Algorithm and Number of Equivalence Classes

Harry Joe, Roger Cooke and Dorota Kurowicka
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Harry Joe: Department of Statistics, University of British Columbia, Canada
Dorota Kurowicka: Department of Mathematics, Delft University of Technology, The Netherlands

Chapter 10 in Dependence Modeling:Vine Copula Handbook, 2010, pp 219-231 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractA natural order for a regular vine on n variables is an assignment of indices to the variables such that variables indexed with j and j + 1 occur as conditioned variables in a node of tree j, j = 1,…,n−1. Regular vines V and U on n variables are equivalent if there is a permutation π ∈ n! such that π(V) = U. U and V are equivalent if and only if the regular vines in natural order corresponding to U and V are equivalent. The number of equivalence classes for regular vines is obtained by counting the number of equivalence classes for regular vines in natural order.

Keywords: Dependence Modeling; Joint Distributions; Copulae; Vines; Graphical Models; PCC (search for similar items in EconPapers)
Date: 2010
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