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Flexible-dimensional L-statistic for mean estimation of symmetric distributions

Author

Listed:
  • Juan Baz

    (University of Oviedo)

  • Diego García-Zamora

    (University of Jaén)

  • Irene Díaz

    (University of Oviedo)

  • Susana Montes

    (University of Oviedo)

  • Luis Martínez

    (University of Jaén)

Abstract

Estimating the mean of a population is a recurrent topic in statistics because of its multiple applications. If previous data is available, or the distribution of the deviation between the measurements and the mean is known, it is possible to perform such estimation by using L-statistics, whose optimal linear coefficients, typically referred to as weights, are derived from a minimization of the mean squared error. However, such optimal weights can only manage sample sizes equal to the one used to derive them, while in real-world scenarios this size might slightly change. Therefore, this paper proposes a method to overcome such a limitation and derive approximations of flexible-dimensional optimal weights. To do so, a parametric family of functions based on extreme value reductions and amplifications is proposed to be adjusted to the cumulative optimal weights of a given sample from a symmetric distribution. Then, the application of Yager’s method to derive weights for ordered weighted average (OWA) operators allows computing the approximate optimal weights for sample sizes close to the original one. This method is justified from the theoretical point of view by proving a convergence result regarding the cumulative weights obtained for different sample sizes. Finally, the practical performance of the theoretical results is shown for several classical symmetric distributions.

Suggested Citation

  • Juan Baz & Diego García-Zamora & Irene Díaz & Susana Montes & Luis Martínez, 2024. "Flexible-dimensional L-statistic for mean estimation of symmetric distributions," Statistical Papers, Springer, vol. 65(7), pages 4001-4024, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01547-z
    DOI: 10.1007/s00362-024-01547-z
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    References listed on IDEAS

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    1. Alex Dytso & Ronit Bustin & H. Vincent Poor & Shlomo Shamai, 2018. "Analytical properties of generalized Gaussian distributions," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-40, December.
    2. Peng Ding, 2014. "Three Occurrences of the Hyperbolic-Secant Distribution," The American Statistician, Taylor & Francis Journals, vol. 68(1), pages 32-35, February.
    3. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    4. Hisham M. Almongy & Ehab M. Almetwally & Randa Alharbi & Dalia Alnagar & E. H. Hafez & Marwa M. Mohie El-Din & Ahmed Mostafa Khalil, 2021. "The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data," Complexity, Hindawi, vol. 2021, pages 1-15, February.
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