Best finite constrained approximations of one-dimensional probabilities

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • Chuang Xu
  • Arno Berger

This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the L r -Kantorovich (or transport) distance, where either the locations or the weights of the approximations’ atoms are prescribed. Necessary and sufficient optimality conditions are established, and the rate of convergence (as the number of atoms goes to infinity) is discussed. In view of emerging mathematical and statistical applications, special attention is given to the case of best uniform approximations (i.e., all atoms having equal weight). The approach developed in this paper is elementary; it is based on best approximations of (monotone) L r -functions by step functions, and thus different from, yet naturally complementary to, the classical Voronoi partition approach.

OriginalsprogEngelsk
TidsskriftJournal of Approximation Theory
Vol/bind244
Sider (fra-til)1-36
Antal sider36
ISSN0021-9045
DOI
StatusUdgivet - 2019

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