Dependence Properties of B-Spline Copulas

Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

Research output: Contribution to journalArticle

Abstract

We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker’s distributions. The range of correlation of the B-spline copulas is examined, and the Fréchet–Hoeffding upper bound is proved to be attained when the number of B-spline functions goes to infinity. As the B-spline functions are well-known to be an order-complete weak Tchebycheff system from which the property of total positivity of any order follows for the maximum correlation case, the results given here extend classical results for the Bernstein copulas. In addition, we derive in terms of the Stirling numbers of the second kind an explicit formula for the moments of the related B-spline functions on the right half-line.

Original languageEnglish (US)
JournalSankhya A
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

B-spline Function
Copula
B-spline
Total Positivity
Stirling numbers of the second kind
Half line
Explicit Formula
Infinity
Upper bound
Moment
Range of data

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Dou, Xiaoling ; Kuriki, Satoshi ; Lin, Gwo Dong ; Richards, Donald. / Dependence Properties of B-Spline Copulas. In: Sankhya A. 2019.
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Dependence Properties of B-Spline Copulas. / Dou, Xiaoling; Kuriki, Satoshi; Lin, Gwo Dong; Richards, Donald.

In: Sankhya A, 01.01.2019.

Research output: Contribution to journalArticle

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