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A class of asymptotically efficient estimators based on sample spacings
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
2019 (English)In: Test (Madrid), ISSN 1133-0686, E-ISSN 1863-8260Article in journal (Refereed) Epub ahead of print
Abstract [en]

In this paper, we consider general classes of estimators based on higher-order sample spacings, called the Generalized Spacings Estimators. Such classes of estimators are obtained by minimizing the Csiszár divergence between the empirical and true distributions for various convex functions, include the “maximum spacing estimators” as well as the maximum likelihood estimators (MLEs) as special cases, and are especially useful when the latter do not exist. These results generalize several earlier studies on spacings-based estimation, by utilizing non-overlapping spacings that are of an order which increases with the sample size. These estimators are shown to be consistent as well as asymptotically normal under a fairly general set of regularity conditions. When the step size and the number of spacings grow with the sample size, an asymptotically efficient class of estimators, called the “Minimum Power Divergence Estimators,” are shown to exist. Simulation studies give further support to the performance of these asymptotically efficient estimators in finite samples and compare well relative to the MLEs. Unlike the MLEs, some of these estimators are also shown to be quite robust under heavy contamination.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2019.
Keywords [en]
Sample spacings, Estimation, Asymptotic efficiency, Robustness
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-163292DOI: 10.1007/s11749-019-00637-7Scopus ID: 2-s2.0-85069960299OAI: oai:DiVA.org:umu-163292DiVA, id: diva2:1350874
Available from: 2019-09-12 Created: 2019-09-12 Last updated: 2019-09-16

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Ekström, Magnus

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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Language
  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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  • asciidoc
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