Dependence Properties of B-Spline Copulas

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

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)283-311
ページ数29
ジャーナルSankhya A
83
1
DOI
出版ステータスPublished - 2021 2

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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