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MEASURES OF CONCORDANCE OF POLYNOMIAL TYPE
 Date Issued:
 2004
 Abstract/Description:
 A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2copulas. 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 $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau.
Title:  MEASURES OF CONCORDANCE OF POLYNOMIAL TYPE. 
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Name(s): 
Edwards, Heather, Author Taylor, Michael , Committee Chair University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2004  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2copulas. 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 $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau.  
Identifier:  CFE0000254 (IID), ucf:46231 (fedora)  
Note(s): 
20041201 Ph.D. Arts and Sciences, Department of Mathematics Doctorate This record was generated from author submitted information. 

Subject(s): 
measure of concordance copula 

Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0000254  
Restrictions on Access:  campus 20140131  
Host Institution:  UCF 