Dependence Properties of B-Spline Copulas

Xiaoling Dou (), Satoshi Kuriki (), Gwo Dong Lin () and Donald Richards ()
Additional contact information
Xiaoling Dou: Waseda University
Satoshi Kuriki: The Institute of Statistical Mathematics
Gwo Dong Lin: Academia Sinica
Donald Richards: Pennsylvania State University

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 12, 283-311

Abstract: 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.

Keywords: Bernstein copula; Fréchet–Hoeffding upper bound; Order-complete weak Tchebycheff system; Schur function; Stirling number of the second kind; Total positivity of order r.; Primary 62H20; 62G30; 41A15 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-019-00179-y

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