Measures Of Concordance Of Polynomial Type

A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on (0,1)²ⁿ is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in d_n. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in d₂ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in d₂ as well as Kendall's tau.

Author dc:creator

• Edwards, Heather

Contributors dc:contributor

• Taylor, Michael

• measure of concordance
• copula
• Mathematics

Language dc:language

English

Identifier

CFE0000254

OAI identifier oai:identifier

oai:stars.library.ucf.edu:etd-1184