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On minimum Kantorovich distance estimators

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  • Bassetti, Federico
  • Bodini, Antonella
  • Regazzini, Eugenio

Abstract

This article introduces estimators defined as minimizers of Kantorovich distances between statistical models and empirical distributions. Existence, measurability and consistency of these estimators are studied. A few significant examples illustrate the applicability of the theoretical results dealt with in the paper.

Suggested Citation

  • Bassetti, Federico & Bodini, Antonella & Regazzini, Eugenio, 2006. "On minimum Kantorovich distance estimators," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1298-1302, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1298-1302
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    References listed on IDEAS

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    1. Sándor Csörgö, 2002. "Weighted correlation tests for scale families," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 219-248, June.
    2. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
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    Cited by:

    1. Manuel Arellano & Stéphane Bonhomme, 2023. "Recovering Latent Variables by Matching," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 693-706, January.
    2. Espen Bernton & Pierre E. Jacob & Mathieu Gerber & Christian P. Robert, 2019. "Approximate Bayesian computation with the Wasserstein distance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 235-269, April.
    3. Shun-ichi Amari & Takeru Matsuda, 2022. "Wasserstein statistics in one-dimensional location scale models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 33-47, February.
    4. Morgan A. Schmitz & Matthieu Heitz & Nicolas Bonneel & Fred Ngolè & David Coeurjolly, 2017. "Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning," Working Papers 2017-84, Center for Research in Economics and Statistics.
    5. Emanuele Dolera, 2022. "Preface to the Special Issue on “Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini’s 75th Birthday”," Mathematics, MDPI, vol. 10(15), pages 1-4, July.
    6. Combes, Catherine & Ng, Hon Keung Tony, 2022. "On parameter estimation for Amoroso family of distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 309-327.
    7. Aude Geneway & Gabriel Peyré & Marco Cuturi, 2017. "Learning Generative Models with Sinkhorn Divergences," Working Papers 2017-83, Center for Research in Economics and Statistics.

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