IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i1d10.1007_s11009-024-10132-8.html
   My bibliography  Save this article

Randomized Repeated Significance Tests Based on Scan Statistics for Discrete Data

Author

Listed:
  • Yong Qiao

    (University of Connecticut)

  • Joseph Glaz

    (University of Connecticut)

Abstract

In this article we introduce randomized repeated significance tests (RSTs), based on scan statistics, for detecting a local change in a parameter of a distribution for one and two dimensional discrete data. When the size of the window where a local change in the parameter has occurred is known, a randomized RST based on a fixed window scan statistic is proposed. When the size of the window where a local change in the parameter has occurred is unknown, a randomized RST based on the minimum P-value scan statistic is developed. Simulation based methods are used to implement these randomized RSTs. Numerical results for one and two dimensional data, generated from Bernoulli and Poisson distributions, for selected values of model parameters, demonstrate the effectiveness of the randomized RSTs in detecting a local change in the parameter of the respective model.

Suggested Citation

  • Yong Qiao & Joseph Glaz, 2025. "Randomized Repeated Significance Tests Based on Scan Statistics for Discrete Data," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-26, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-024-10132-8
    DOI: 10.1007/s11009-024-10132-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10132-8
    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/s11009-024-10132-8?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. Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
    2. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
    3. Karwe, Vatsala V. & Naus, Joseph I., 1997. "New recursive methods for scan statistic probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 23(3), pages 389-402, January.
    4. Joseph Glaz & Joseph Naus & Xiao Wang, 2012. "Approximations and Inequalities for Moving Sums," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 597-616, September.
    5. Hanmin Guo & James J. Li & Qiongshi Lu & Lin Hou, 2021. "Detecting local genetic correlations with scan statistics," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    6. Miao, Congcong & Chen, Xiang & Zhang, Chuanrong, 2024. "Assessing network-based traffic crash risk using prospective space-time scan statistic method," Journal of Transport Geography, Elsevier, vol. 119(C).
    7. G. Haiman & C. Preda, 2006. "Estimation for the Distribution of Two-dimensional Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 373-382, September.
    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. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.
    2. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
    3. Haiman, George & Preda, Cristian, 2013. "One dimensional scan statistics generated by some dependent stationary sequences," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1457-1463.
    4. Qianzhu Wu & Joseph Glaz, 2021. "Scan Statistics for Normal Data with Outliers," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 429-458, March.
    5. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    6. Wu, Tung-Lung & Glaz, Joseph, 2015. "A new adaptive procedure for multiple window scan statistics," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 164-172.
    7. Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, October.
    8. Carey E. Priebe & John M. Conroy & David J. Marchette & Youngser Park, 2005. "Scan Statistics on Enron Graphs," Computational and Mathematical Organization Theory, Springer, vol. 11(3), pages 229-247, October.
    9. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. Jack Noonan & Anatoly Zhigljavsky, 2021. "Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 873-892, September.
    11. Joseph Glaz & Marco Guerriero & Rohini Sen, 2010. "Approximations for a Three Dimensional Scan Statistic," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 731-747, December.
    12. Bo Zhao & Joseph Glaz, 2016. "Scan Statistics for Detecting a Local Change in Variance for Normal Data with Known Variance," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 563-573, June.
    13. Tung-Lung Wu, 2020. "Conditional waiting time distributions of runs and patterns and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 531-543, April.
    14. Wang, Xiao & Zhao, Bo & Glaz, Joseph, 2014. "A multiple window scan statistic for time series models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 196-203.
    15. Chen, Jie & Glaz, Joseph, 2002. "Approximations for a conditional two-dimensional scan statistic," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 287-296, July.
    16. Hisashi Yamamoto & Tomoaki Akiba, 2005. "Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 243-252, April.
    17. Bartolucci, F., 2001. "Developments of the Markov chain approach within the distribution theory of runs," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 107-118, March.
    18. Dafnis, Spiros D. & Makri, Frosso S. & Philippou, Andreas N., 2019. "The reliability of a generalized consecutive system," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 186-193.
    19. Morteza Ebneshahrashoob & Tangan Gao & Mengnien Wu, 2005. "An Efficient Algorithm for Exact Distribution of Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 459-471, December.
    20. Zhao, Bo & Glaz, Joseph, 2016. "Scan statistics for detecting a local change in variance for normal data with unknown population variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 137-145.

    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:metcap:v:27:y:2025:i:1:d:10.1007_s11009-024-10132-8. 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.