IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v32y2023i1d10.1007_s11749-022-00831-0.html
   My bibliography  Save this article

Some parametric tests based on sample spacings

Author

Listed:
  • Rahul Singh

    (Indian Institute of Technology Kanpur)

  • Neeraj Misra

    (Indian Institute of Technology Kanpur)

Abstract

Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on statistics that are symmetric functions of m-step disjoint sample spacings. Asymptotic properties of these tests have been investigated under the simple null hypothesis and under a sequence of local alternatives converging to the null hypothesis. The asymptotic properties of the proposed tests have also been studied under the composite null hypothesis. We observed that these tests have similar asymptotic properties as the likelihood ratio test. Finite sample performances of the proposed tests are assessed numerically. A data analysis based on real data is also reported. The proposed tests provide alternative to similar tests based on simple spacings (i.e. $$m=1$$ m = 1 ), that were proposed earlier in the literature. These tests also provide an alternative to likelihood ratio tests in situations where likelihood function may be unbounded, and hence, likelihood ratio tests do not exist.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00831-0
    DOI: 10.1007/s11749-022-00831-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00831-0
    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/s11749-022-00831-0?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Torabi, Hamzeh, 2006. "A new method for hypotheses testing using spacings," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1345-1347, July.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. Sherzod Mirakhmedov & Syed Tirmizi & Muhammad Naeem, 2011. "A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 33-54, July.
    5. S. M. Mirakhmedov & S. Rao Jammalamadaka & Ibrahim B. Mohamed, 2014. "On Edgeworth Expansions in Generalized Urn Models," Journal of Theoretical Probability, Springer, vol. 27(3), pages 725-753, September.
    6. Ibrahim Bin Mohamed & Sherzod M. Mirakhmedov, 2016. "Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 188-220, August.
    7. Magnus Ekström, 2013. "Powerful Parametric Tests Based on Sum-Functions of Spacings," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 886-898, December.
    8. Aya-Moreno, Carlos & Geenens, Gery & Penev, Spiridon, 2018. "Shape-preserving wavelet-based multivariate density estimation," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 30-47.
    9. Singh, Rahul, 2023. "Some goodness of fit tests based on centre outward spacings," Statistics & Probability Letters, Elsevier, vol. 194(C).

    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:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00831-0. 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.