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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 312–330 (Mi tvp109)  

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic properties and robustness of minimum dissimilarity estimators of location-scale parameters

F. Bassetti, E. Regazzini

Dipartimento di Matematica dell'Università di Pavia

Abstract: This paper deals with the asymptotic properties of an unexplored estimation method, for location and scale parameters, based on the minimization of the Monge–Gini–Kantorovich–Wasserstein distance. This method is rigorously defined and justified according to the general principle which directs the theory of regression. The resulting estimators — called minimum dissimilarity estimators — exist, and are measurable, consistent, and robust. Their asymptotic distribution is the same as the probability distribution of the absolute minimum point of an interesting functional of a standard Brownian bridge. This fact can be employed to obtain both explicit exact expressions and numerical approximations for the above asymptotic distribution.

Keywords: argmax argument, asymptotic laws, influence function, minimum dissimilarity estimator, Monge–Gini–Kantorovich–Wasserstein metric, occupation time of a Brownian bridge, robustness, minimum dissimilarity estimators.

DOI: https://doi.org/10.4213/tvp109

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English version:
Theory of Probability and its Applications, 2006, 50:2, 171–186

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Received: 09.12.2004
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Citation: F. Bassetti, E. Regazzini, “Asymptotic properties and robustness of minimum dissimilarity estimators of location-scale parameters”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 312–330; Theory Probab. Appl., 50:2 (2006), 171–186

Citation in format AMSBIB
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\pages 312--330
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\transl
\jour Theory Probab. Appl.
\yr 2006
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\issue 2
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bassetti F., Bodini A., Regazzini E., “On minimum Kantorovich distance estimators”, Statist. Probab. Lett., 76:12 (2006), 1298–1302  crossref  mathscinet  zmath  isi  scopus
    2. Schmitz M.A., Heitz M., Bonneel N., Ngole F., Coeurjolly D., Cuturi M., Peyre G., Starck J.-L., “Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning”, SIAM J. Imaging Sci., 11:1 (2018), 643–678  crossref  mathscinet  isi  scopus
    3. Auricchio G., Gualandi S., Veneroni M., Bassetti F., Advances in Neural Information Processing Systems 31 (Nips 2018), Advances in Neural Information Processing Systems, 31, eds. Bengio S., Wallach H., Larochelle H., Grauman K., CesaBianchi N., Garnett R., Neural Information Processing Systems (Nips), 2018  isi
    4. Bernton E., Jacob P.E., Gerber M., Robert Ch.P., “On Parameter Estimation With the Wasserstein Distance”, Inf. Inference, 8:4 (2019), 657–676  crossref  mathscinet  isi
    5. Bassetti F., Gualandi S., Veneroni M., “On the Computation of Kantorovich Wasserstein Distances Between Two-Dimensional Histograms By Uncapacitated Minimum Cost Flows”, SIAM J. Optim., 30:3 (2020), 2441–2469  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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