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Published in:
2015 | OriginalPaper | Chapter
A New Measure of Monotone Dependence by Using Sobolev Norms for Copula
Authors : Hien D. Tran, Uyen H. Pham, Sel Ly, T. Vo-Duy
Published in: Integrated Uncertainty in Knowledge Modelling and Decision Making
Publisher: Springer International Publishing
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Dependence structure, e.g. measures of dependence, is one of the main studies in correlation analysis. In [10], B. Schweizer and E.F. Wolff used L
p
-metric
$d_{L^{p}}(C,P)$
to obtain a measure of monotone dependence where
P
is the product copula or independent copula, and in [11] P. A. Stoimenov defined Sobolev metric
d
S
(
C
,
P
) to construct the measure
ω
(
C
) for a class of Mutual Complete Dependences (MCDs). Due to the fact that the class of monotone dependence is contained in the class of MCDs, we constructed a new measure of monotone dependence,
λ
(
C
), based on Sobolev metric which can be used to characterize comonotonic, countermonotonic and independence.