IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i6d10.1007_s00362-022-01377-x.html
   My bibliography  Save this article

A class of estimators based on overlapping sample spacings

Author

Listed:
  • Rahul Singh

    (Indian Institute of Technology Kanpur)

  • Neeraj Misra

    (Indian Institute of Technology Kanpur)

Abstract

In parametric models, minimising different estimators of the Kullback–Leibler divergence between the empirical distribution function and the true distribution function yield the maximum likelihood estimator (MLE) and the maximum spacings product estimator. This approach has been extended in the literature to minimise some estimators of Csisźar divergence between the empirical distribution function and the true distribution function. Such estimators based on disjoint spacings have recently been studied in the literature. This paper considers analogues of these estimators based on overlapping sample spacings. The estimators have been found to be consistent and asymptotically normally distributed under a broad set of regularity conditions. Asymptotically and for any fixed order of spacings, such estimators are at least as good as the corresponding estimators based on non-overlapping spacings. Simulation studies show that some of these estimators perform better than the MLE for contaminated models. An application to real data reveals that the considered estimators can perform better than the MLE for parsimonious models.

Suggested Citation

  • Rahul Singh & Neeraj Misra, 2023. "A class of estimators based on overlapping sample spacings," Statistical Papers, Springer, vol. 64(6), pages 2137-2160, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01377-x
    DOI: 10.1007/s00362-022-01377-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01377-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01377-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Manisha & M. MASOOM ALI & JUNGSOO WOO, 2006. "Exponentiated Weibull distribution," Statistica, Department of Statistics, University of Bologna, vol. 66(2), pages 139-147.
    2. 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.
    3. 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.
    4. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kristi Kuljus & Bo Ranneby, 2025. "Maximum spacing estimation for hidden Markov models," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-31, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Kristi Kuljus & Bo Ranneby, 2021. "Maximum spacing estimation for continuous time Markov chains and semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 421-443, July.
    3. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum product of spacings prediction of future record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 853-868, October.
    4. Kristi Kuljus & Bo Ranneby, 2025. "Maximum spacing estimation for hidden Markov models," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-31, April.
    5. 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.
    6. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    7. Arun Kumar Kuchibhotla & Somabha Mukherjee & Ayanendranath Basu, 2019. "Statistical inference based on bridge divergences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 627-656, June.
    8. Kristi Kuljus & Bo Ranneby, 2020. "Asymptotic normality of generalized maximum spacing estimators for multivariate observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 968-989, September.
    9. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    10. 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.
    11. R. Jiménez & J. E. Yukich, 2002. "Asymptotics for Statistical Distances Based on Voronoi Tessellations," Journal of Theoretical Probability, Springer, vol. 15(2), pages 503-541, April.
    12. Liu, Yan, 2017. "Robust parameter estimation for stationary processes by an exotic disparity from prediction problem," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 120-130.
    13. A. Philip Dawid & Monica Musio & Laura Ventura, 2016. "Minimum Scoring Rule Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 123-138, March.
    14. Suparna Basu & Sanjay Kumar Singh & Umesh Singh, 2017. "Parameter estimation of inverse Lindley distribution for Type-I censored data," Computational Statistics, Springer, vol. 32(1), pages 367-385, March.
    15. Abhijit Mandal & Beste Hamiye Beyaztas & Soutir Bandyopadhyay, 2023. "Robust density power divergence estimates for panel data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 773-798, October.
    16. Ehab M. Almetwally & Hanan A. Haj Ahmad, 2020. "A new generalization of the Pareto distribution and its applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(5), pages 61-84, December.
    17. Paola Stolfi & Mauro Bernardi & Davide Vergni, 2022. "Robust estimation of time-dependent precision matrix with application to the cryptocurrency market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    18. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    19. Cesar Augusto Taconeli & Idemauro Antonio Rodrigues Lara, 2022. "Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach," Computational Statistics, Springer, vol. 37(5), pages 2267-2293, November.
    20. Md. Mahabubur Rahman & Bander Al-Zahrani & Muhammad Qaiser Shahbaz, 2019. "Cubic Transmuted Weibull Distribution: Properties and Applications," Annals of Data Science, Springer, vol. 6(1), pages 83-102, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01377-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.