IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v14y2012i3d10.1007_s11009-011-9251-x.html
   My bibliography  Save this article

Approximations and Inequalities for Moving Sums

Author

Listed:
  • Joseph Glaz

    (University of Connecticut)

  • Joseph Naus

    (The State University of New Jersey)

  • Xiao Wang

    (University of Connecticut)

Abstract

In this article accurate approximations and inequalities are derived for the distribution, expected stopping time and variance of the stopping time associated with moving sums of independent and identically distributed continuous random variables. Numerical results for a scan statistic based on a sequence of moving sums are presented for a normal distribution model, for both known and unknown mean and variance. The new R algorithms for the multivariate normal and t distributions established by Genz et al. (2010) provide readily available numerical values of the bounds and approximations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9251-x
    DOI: 10.1007/s11009-011-9251-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-011-9251-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/s11009-011-9251-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 search for a different version of it.

    References listed on IDEAS

    as
    1. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
    2. Anders Westlund, 1984. "Sequential moving sums of squares of OLS residuals in parameter stability testing," Quality & Quantity: International Journal of Methodology, Springer, vol. 18(3), pages 261-273, May.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Anat Reiner-Benaim, 2016. "Scan Statistic Tail Probability Assessment Based on Process Covariance and Window Size," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 717-745, September.
    9. 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.

    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. 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.
    3. 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.
    4. Alexandru Amărioarei & Cristian Preda, 2015. "Approximation for the Distribution of Three-dimensional Discrete Scan Statistic," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 565-578, September.
    5. 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.
    6. George Haiman & Cristian Preda, 2010. "A New Method of Approximating the Probability of Matching Common Words in Multiple Random Sequences," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 775-795, December.
    7. George Haiman, 2012. "1-Dependent Stationary Sequences for Some Given Joint Distributions of Two Consecutive Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 445-458, September.
    8. 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.
    9. G. Haiman & C. Preda, 2002. "A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 393-407, December.

    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:14:y:2012:i:3:d:10.1007_s11009-011-9251-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.