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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.
2018 (English)In: The 27th Nordic Conference in Mathematical Statistics: Abstracts, 2018Conference paper, Oral presentation with published abstract (Other academic)
Abstract [en]

We consider general classes of estimators based on higher-order sample spacings,called Generalized Spacings Estimators (GSEs). Such classes of estimators areobtained by minimizing approximations of Csisz´ar divergences between distributionsin the model and the true underlying distribution; maximum likelihood estimators(MLEs) may be derived in a similar way using the Kullback-Leibler divergence. Ourresults generalize several earlier studies on spacings-based estimation, by utilizingnon-overlapping spacings that are of an order which increases with the sample size.The GSEs are shown to be consistent as well as asymptotically normal under a fairlygeneral set of regularity conditions. When both the order of the spacings and thenumber of spacings grow with the sample size, an asymptotically efficient class ofestimators, called the “Minimum Power Divergence Estimators,” are shown to exist.Simulation studies give further support to the performance of these asymptoticallyefficient estimators in finite samples, and compare well relative to the MLEs as wellas corresponding estimators based on “overlapping” higher order spacings. Unlikethe MLEs, some of these estimators are also shown to be quite robust under heavycontamination.

Place, publisher, year, edition, pages
2018.
Keywords [en]
sample spacings, Csiszár divergences, parametric estimation, asymptotic efficiency, robustness
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-151944OAI: oai:DiVA.org:umu-151944DiVA, id: diva2:1249394
Conference
The 27th Nordic Conference in Mathematical Statistics, June 26 - June 29, 2018, Tartu, Estonia
Available from: 2018-09-19 Created: 2018-09-19 Last updated: 2018-09-19

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Ekström, Magnus

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
  • html
  • text
  • asciidoc
  • rtf