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A class of asymptotically efficient estimators based on sample spacings

Author

Listed:
  • M. Ekström

    (Umeå University
    Swedish University of Agricultural Sciences)

  • S. M. Mirakhmedov

    (Academy of Sciences of Uzbekistan)

  • S. Rao Jammalamadaka

    (University of California)

Abstract

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.

Suggested Citation

  • M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00637-7
    DOI: 10.1007/s11749-019-00637-7
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    References listed on IDEAS

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    1. Sherzod M. Mirakhmedov & S. Rao Jammalamadaka, 2013. "Higher-order expansions and efficiencies of tests based on spacings," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 339-359, June.
    2. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    3. Menéndez, M. & Morales, D. & Pardo, L., 1997. "Maximum entropy principle and statistical inference on condensed ordered data," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 85-93, May.
    4. Yongzhao Shao & Marjorie Hahn, 1999. "Strong Consistency of the Maximum Product of Spacings Estimates with Applications in Nonparametrics and in Estimation of Unimodal Densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 31-49, March.
    5. Kristi Kuljus & Bo Ranneby, 2015. "Generalized Maximum Spacing Estimation for Multivariate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1092-1108, December.
    6. A. Mayoral & D. Morales & J. Morales & I. Vajda, 2003. "On efficiency of estimation and testing with data quantized to fixed number of cells," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 1-27, February.
    7. Mirakhmedov, Sherzod A., 2005. "Lower estimation of the remainder term in the CLT for a sum of the functions of k-spacings," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 411-424, July.
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    Cited by:

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    3. Rahul Singh & Neeraj Misra, 2023. "Some parametric tests based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 211-231, March.

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