Skip to main content
SpringerLink
Log in

Flexible-Dimensional EVR-OWA as Mean Estimator for Symmetric Distributions

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

Abstract

In the field of statistics, linear combinations of order statistics, also known as L-statistics, have been widely used for the estimation of the mean of a population, which is equivalent to considering Ordered Weighted Averaging (OWA) operators over simple random samples. If previous data are available or the distribution of the deviation from the mean is known, it is possible to compute optimal OWA weights that minimize the Mean Squared Error of the estimation. However, the optimal weights can only be used for a specific sample size, while in real Statistics the number of values that must be aggregated may change. In order to overcome this limitation, this contribution proposes a method based on the use of the recently defined Extreme Value Reductions (EVRs) to fit the cumulative optimal OWA weights and then use these EVRs to compute new weights for a different sample size. In addition, theoretical and simulated results are provided to show that, if sample sizes that are similar to the original one are considered, the weights generated by using EVRs are also similar to the optimal ones.

This research has been partially supported by the Spanish Ministry of Science and Technology (TIN-2017-87600-P and PGC2018-098623-B-I00), the Spanish Ministry of Economy and Competitiveness (PGC2018-099402-B-I00) and by the Spanish Ministry of Universities (FPU2019/01203).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahsanullah, M., Alzaatreh, A.: Parameter estimation for the log-logistic distribution based on order statistics. REVSTAT 16(4), 429–443 (2018)

    MathSciNet  MATH  Google Scholar 

  2. Almongy, H.M., Almetwally, E.M., Alharbi, R., Alnagar, D., Hafez, E.H., Mohie El-Din, M.M.: The Weibull generalized exponential distribution with censored sample: estimation and application on real data. Complexity 2021 (2021). Article ID: 6653534

    Google Scholar 

  3. Alzeley, O., Almetwally, E.M., Gemeay, A.M., Alshanbari, H.M., Hafez, E., Abu-Moussa, M.: Statistical inference under censored data for the new exponential-x fréchet distribution: simulation and application to leukemia data. Comput. Intell. Neurosci. 2021 (2021). Article ID: 2167670

    Google Scholar 

  4. Beliakov, G., Bustince Sola, H., Calvo Sánchez, T.: A Practical Guide to Averaging Functions. SFSC, vol. 329. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-24753-3

    Book  Google Scholar 

  5. Calvo, T., Mayor, G., Torrens, J., Suñer, J., Mas, M., Carbonell, M.: Generation of weighting triangles associated with aggregation functions. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 8(04), 417–451 (2000)

    Article  MathSciNet  Google Scholar 

  6. Cramér, H.: A contribution to the theory of statistical estimation. Scand. Actuar. J. 1946(1), 85–94 (1946)

    Article  MathSciNet  Google Scholar 

  7. Dytso, A., Cardone, M., Veedu, M.S., Poor, H.V.: On estimation under noisy order statistics. In: 2019 IEEE International Symposium on Information Theory (ISIT), pp. 36–40. IEEE (2019)

    Google Scholar 

  8. Fréchet, M.: Sur l’extension de certaines évaluations statistiques au cas de petits échantillons. Revue de l’Institut International de Statistique, pp. 182–205 (1943)

    Google Scholar 

  9. Gao, W., Zhang, T., Yang, B.B., Zhou, Z.H.: On the noise estimation statistics. Artif. Intell. 293, 103451 (2021)

    Article  MathSciNet  Google Scholar 

  10. García-Zamora, D., Labella, Á., Rodríguez, R.M., Martínez, L.: Non linear preferences in group decision making. extreme values amplifications and extreme values reductions. Int. J. Intell. Syst. (2021). https://doi.org/10.1002/int.22561

  11. García-Zamora, D., Labella, Á., Rodríguez, R.M., Martín, L.: Symmetric weights for OWA operators prioritizing intermediate values. the EVR-OWA operator. Inf. Sci. 584, 583–602 (2022)

    Article  Google Scholar 

  12. Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  13. Hassan, A.S., Abd-Allah, M.: Exponentiated Weibull-Lomax distribution: properties and estimation. J. Data Sci. 16(2), 277–298 (2018)

    Google Scholar 

  14. Herrera-Viedma, E., Herrera, F., Chiclana, F.: A consensus model for multiperson decision making with different preference structures. IEEE Trans. Syst. Man Cybern. A Syst. Hum. 32, 394–402 (2002). https://doi.org/10.1109/TSMCA.2002.802821

    Article  MATH  Google Scholar 

  15. Klein, J.P., Moeschberger, M.L.: Survival Analysis. SBH, Springer, New York (2003). https://doi.org/10.1007/b97377

    Book  MATH  Google Scholar 

  16. Kumar, D., Kumar, M., Joorel, J.S.: Estimation with modified power function distribution based on order statistics with application to evaporation data. Ann. Data Sci. 1–26 (2020). https://doi.org/10.1007/s40745-020-00244-6

  17. Lloyd, E.: Least-squares estimation of location and scale parameters using order statistics. Biometrika 39(1/2), 88–95 (1952)

    Article  MathSciNet  Google Scholar 

  18. Narisetty, N., Koenker, R.: Censored quantile regression survival models with a cure proportion. J. Econom. 226(1), 192–203 (2022)

    Article  MathSciNet  Google Scholar 

  19. Palomares, I., Estrella, F.J., Martínez, L., Herrera, F.: Consensus under a fuzzy context: Taxonomy, analysis framework AFRYCA and experimental case of study. Inf. Fusion 20, 252–271 (2014)

    Article  Google Scholar 

  20. Radhakrishna Rao, C.: Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37(3), 81–91 (1945)

    MathSciNet  MATH  Google Scholar 

  21. Rohatgi, V.K., Saleh, A.M.E.: An Introduction to Probability and Statistics. Wiley, Hoboken (2015)

    Book  Google Scholar 

  22. Sarhan, A.: Estimation of the mean and standard deviation by order statistics, Part II. Ann. Math. Stat. 26(3), 505–511 (1955)

    Article  Google Scholar 

  23. Sarhan, A.: Estimation of the mean and standard deviation by order statistics, Part III. Ann. Math. Stat. 26(4), 576–592 (1955)

    Google Scholar 

  24. Sarhan, A.E.: Estimation of the mean and standard deviation by order statistics. Ann. Math. Stat. 25(2), 317–328 (1954)

    Google Scholar 

  25. Stephens, M.: Asymptotic calculations of functions of expected values and covariances of order statistics. Can. J. Stat. 18(3), 265–270 (1990)

    Article  MathSciNet  Google Scholar 

  26. Stigler, S.M.: Linear functions of order statistics. Ann. Math. Stat. 40(3), 770–788 (1969)

    Article  MathSciNet  Google Scholar 

  27. Yager, R.: Families of OWA operators. Fuzzy Sets Syst. 59(2), 125–148 (1993)

    Article  MathSciNet  Google Scholar 

  28. Yager, R.: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11(1), 49–73 (1996)

    Article  Google Scholar 

  29. Zadeh, L.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983). https://doi.org/10.1016/0898-1221(83)90013-5

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and O.R. and Mathematics Didactics, University of Oviedo, Oviedo, Spain

    Juan Baz & Susana Montes

  2. Department of Computer Science, University of Jaén, Jaén, Spain

    Diego García-Zamora & Luis Martínez

  3. Department of Computer Science, University of Oviedo, Oviedo, Spain

    Irene Díaz

Authors
  1. Juan Baz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diego García-Zamora
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Irene Díaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Susana Montes
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luis Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Baz .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Baz, J., García-Zamora, D., Díaz, I., Montes, S., Martínez, L. (2022). Flexible-Dimensional EVR-OWA as Mean Estimator for Symmetric Distributions. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08971-8_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation