Best finite constrained approximations of one-dimensional probabilities

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Best finite constrained approximations of one-dimensional probabilities. / Xu, Chuang; Berger, Arno.

I: Journal of Approximation Theory, Bind 244, 2019, s. 1-36.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Xu, C & Berger, A 2019, 'Best finite constrained approximations of one-dimensional probabilities', Journal of Approximation Theory, bind 244, s. 1-36. https://doi.org/10.1016/j.jat.2019.03.005

APA

Xu, C., & Berger, A. (2019). Best finite constrained approximations of one-dimensional probabilities. Journal of Approximation Theory, 244, 1-36. https://doi.org/10.1016/j.jat.2019.03.005

Vancouver

Xu C, Berger A. Best finite constrained approximations of one-dimensional probabilities. Journal of Approximation Theory. 2019;244:1-36. https://doi.org/10.1016/j.jat.2019.03.005

Author

Xu, Chuang ; Berger, Arno. / Best finite constrained approximations of one-dimensional probabilities. I: Journal of Approximation Theory. 2019 ; Bind 244. s. 1-36.

Bibtex

@article{e9cd444c5f7c499da29db568227a65e7,
title = "Best finite constrained approximations of one-dimensional probabilities",
abstract = " 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{\textquoteright} 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. ",
keywords = "Asymptotically best approximation, Balanced function, Best uniform approximation, Constrained approximation, Kantorovich distance, Quantile function",
author = "Chuang Xu and Arno Berger",
year = "2019",
doi = "10.1016/j.jat.2019.03.005",
language = "English",
volume = "244",
pages = "1--36",
journal = "Journal of Approximation Theory",
issn = "0021-9045",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Best finite constrained approximations of one-dimensional probabilities

AU - Xu, Chuang

AU - Berger, Arno

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Asymptotically best approximation

KW - Balanced function

KW - Best uniform approximation

KW - Constrained approximation

KW - Kantorovich distance

KW - Quantile function

UR - http://www.scopus.com/inward/record.url?scp=85063510131&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2019.03.005

DO - 10.1016/j.jat.2019.03.005

M3 - Journal article

AN - SCOPUS:85063510131

VL - 244

SP - 1

EP - 36

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

ER -

ID: 222751608