Smooth Cyclically Monotone Interpolation and Empirical Center-Outward Distribution Functions
Eustasio Del Barrio,
Juan Cuesta Albertos,
Marc Hallin () and
No 2018-15, Working Papers ECARES from ULB -- Universite Libre de Bruxelles
We consider the smooth interpolation problem under cyclical monotonicity constraint. More precisely, consider finite n-tuples X =fx1; xng and Y = fy1; yng of points in Rd, and assume the existence of a unique bijection T :X !Y such that f(x; T(x)): x 2 Xg is cyclically monotone: our goal is to define continuous, cyclically mono-tone maps T :Rd !Rd such that T(xi) = yi, i = 1; n, extending a classical result by Rockafellar on the sub differentials of convex functions. Our solutions T are Lipschitz, and we provide a sharp lower bound for the corresponding Lipschitz constants. The problem is motivated by, and the solution naturally applies to, the concept of empirical center-outwarddistribution function in Rd developed in Hallin (2018). Those empirical distribution functions indeed are de_ned at the observations only. Our interpolation provides a smooth extension, as well as a multivariate, outward-continuous, jump function version thereof (the latter naturally generalizes the traditional left-continuous univariate concept); both satisfy a Glivenko-Cantelli property as n !1.
New Economics Papers: this item is included in nep-mac
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/2713 ... IN_MATRAN-smooth.pdf Œuvre complète ou partie de l'œuvre (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2013/271399
Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/271399
Access Statistics for this paper
More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().