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A class of asymptotically efficient estimators based on sample spacings
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
2018 (engelsk)Inngår i: The 27th Nordic Conference in Mathematical Statistics: Abstracts, 2018Konferansepaper, Oral presentation with published abstract (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
2018.
Emneord [en]
sample spacings, Csiszár divergences, parametric estimation, asymptotic efficiency, robustness
HSV kategori
Forskningsprogram
statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-151944OAI: oai:DiVA.org:umu-151944DiVA, id: diva2:1249394
Konferanse
The 27th Nordic Conference in Mathematical Statistics, June 26 - June 29, 2018, Tartu, Estonia
Tilgjengelig fra: 2018-09-19 Laget: 2018-09-19 Sist oppdatert: 2018-09-19

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