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A class of asymptotically efficient estimators based on sample spacings

  • M. Ekström [1] ; S. M. Mirakhmedov [3] ; S. Rao Jammalamadaka [2]
    1. [1] Swedish University of Agricultural Sciences

      Swedish University of Agricultural Sciences

      Uppsala domkyrkoförs., Suecia

    2. [2] University of California, Santa Barbara

      University of California, Santa Barbara

      Estados Unidos

    3. [3] Department of Probability and Statistics, Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
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  • Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 3, 2020, págs. 617-636
  • Idioma: inglés
  • DOI: 10.1007/s11749-019-00637-7
  • Texto completo no disponible (Saber más ...)
  • Resumen

    • 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.

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