Approximations for a conditional two-dimensional scan statistic
AbstractLet Xi,j,1[less-than-or-equals, slant]i[less-than-or-equals, slant]n1,1[less-than-or-equals, slant]j[less-than-or-equals, slant]n2, be a sequence of independent and identically distributed nonnegative integer valued random variables. The observation Xi,j denotes the number of events that have occurred in the i,jth location in a two dimensional rectangular region R. For 2[less-than-or-equals, slant]mi[less-than-or-equals, slant]ni-1, i=1,2, the two dimensional discrete scan statistic is defined as the maximum number of events in any of the m1 by m2 consecutive rectangular windows in that region. Conditional on the total number of events that have occurred in R, we refer to this scan statistic as the conditional two-dimensional scan statistic. Two-dimensional scan statistics have been extensively used in many areas of science to analyze the occurrence of observed clusters of events in space. Since this scan statistic is based on highly dependent consecutive subsequences of observed data, accurate approximations for its distributions are of great value. In this article, based on the scanning window representation of the scan statistic, accurate product-type, Poisson and a compound Poisson approximations are investigated. Moreover, accurate approximations for the expected size of the scan statistic are derived. Numerical results are presented to evaluate the performance of the approximations discussed in this article.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 58 (2002)
Issue (Month): 3 (July)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
- James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer, vol. 46(1), pages 179-192, March.
- Seneta, Eugene & Chen, John T., 2005. "A generator for explicit univariate lower bounds," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 256-266, December.
- Glaz, Joseph & Zhang, Zhenkui, 2006. "Maximum scan score-type statistics," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1316-1322, July.
If references are entirely missing, you can add them using this form.