Regular vines with strongly chordal pattern of (conditional) independence

Abstract

Multivariate statistical models can be simplified by assuming that a pattern of conditional independence is presented in the given data. A popular way of capturing the (conditional) independence is to use probabilistic graphical models. The relationship between strongly chordal graphs and m-saturated vines is proved. Moreover, an algorithm to construct an m-saturated vine structure corresponding to strongly chordal graph is provided. This allows the reduction of regular vine copula models complexity. When the underlying data is sparse our approach leads to model estimation improvement when compared with current heuristic methods. Furthermore, due to reduction of model complexity it is possible to evaluate all vine structures as well as to fit non-simplified vines. These advantages have been shown in the simulated and real data examples.¹