IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i4p725-757.html
   My bibliography  Save this article

Approximate tail probabilities of the maximum of a chi-square field on multi-dimensional lattice points and their applications to detection of loci interactions

Author

Listed:
  • Satoshi Kuriki
  • Yoshiaki Harushima
  • Hironori Fujisawa
  • Nori Kurata

Abstract

In this study, we define a chi-square random field on a multi-dimensional lattice points index set with a direct product covariance structure and consider the distribution of the maximum of this random field. We provide two approximate formulas for the upper tail probability of the distribution based on nonlinear renewal theory and an integral-geometric approach called the volume-of-tube method. This study is motivated by the detection problem of the interactive loci pairs which play an important role in forming biological species. The joint distribution of scan statistics for detecting the pairs is regarded as the chi-square random field above, and hence the multiplicity-adjusted $$p$$ p -value can be calculated using the proposed approximate formulas. By using these formulas, we examine the data of Mizuta, Harushima and Kurata (Proc Nat Acad Sci USA 107(47):20417–20422, 2010 ) who reported a new interactive loci pair of rice inter-subspecies. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Satoshi Kuriki & Yoshiaki Harushima & Hironori Fujisawa & Nori Kurata, 2014. "Approximate tail probabilities of the maximum of a chi-square field on multi-dimensional lattice points and their applications to detection of loci interactions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 725-757, August.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:4:p:725-757
    DOI: 10.1007/s10463-013-0419-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0419-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0419-8?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. David Siegmund, 2004. "Model selection in irregular problems: Applications to mapping quantitative trait loci," Biometrika, Biometrika Trust, vol. 91(4), pages 785-800, December.
    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. Pan, Jianmin & Chen, Jiahua, 2006. "Application of modified information criterion to multiple change point problems," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2221-2241, November.
    2. Yoshiyuki Ninomiya, 2015. "Change-point model selection via AIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 943-961, October.
    3. Nancy R. Zhang & David O. Siegmund, 2007. "A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data," Biometrics, The International Biometric Society, vol. 63(1), pages 22-32, March.
    4. Yoshiyuki Ninomiya & Hironori Fujisawa, 2007. "A Conservative Test for Multiple Comparison Based on Highly Correlated Test Statistics," Biometrics, The International Biometric Society, vol. 63(4), pages 1135-1142, December.
    5. Yawei He & Zehua Chen, 2016. "The EBIC and a sequential procedure for feature selection in interactive linear models with high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 155-180, February.
    6. Chun Wang, 2021. "Using Penalized EM Algorithm to Infer Learning Trajectories in Latent Transition CDM," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 167-189, March.
    7. Baierl, Andreas & Futschik, Andreas & Bogdan, Malgorzata & Biecek, Przemyslaw, 2007. "Locating multiple interacting quantitative trait loci using robust model selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6423-6434, August.
    8. Ryoto Ozaki & Yoshiyuki Ninomiya, 2023. "Information criteria for detecting change‐points in the Cox proportional hazards model," Biometrics, The International Biometric Society, vol. 79(4), pages 3050-3065, December.
    9. Jian Li & Fugee Tsung & Changliang Zou, 2013. "Directional change‐point detection for process control with multivariate categorical data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 160-173, March.
    10. Wang, Tao & Zhu, Lixing, 2011. "Consistent tuning parameter selection in high dimensional sparse linear regression," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1141-1151, August.
    11. Shan Luo & Jinfeng Xu & Zehua Chen, 2015. "Extended Bayesian information criterion in the Cox model with a high-dimensional feature space," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 287-311, April.

    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:aistmt:v:66:y:2014:i:4:p:725-757. 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.