Skip to main content
SpringerLink
Log in

Variable Window Scan Statistics: Alternatives to Generalized Likelihood Ratio Tests

  • Living reference work entry
  • First Online:
Handbook of Scan Statistics

Abstract

Classical variable window scan statistics are based on likelihood ratios issued from parametric models. However, these likelihood ratios do not give equal chances to all potential clusters. I introduce alternatives which do not suffer the same problem and describe their properties. I apply these methods to a classical epidemiological data set.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  • Cucala L (2008) A hypothesis-free multiple scan statistic with variable window. Biom J 50: 299–310

    Article  MathSciNet  Google Scholar 

  • Cucala L (2014) A distribution-free spatial scan statistic for marked point processes. Spat Stat 10:117–125

    Article  MathSciNet  Google Scholar 

  • Cucala L (2016) A Mann-Whitney scan statistic for marked point processes. Commun Stat Theory and Methods 45:321–329

    Article  MathSciNet  MATH  Google Scholar 

  • Diggle P (1990) A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point. J R Stat Soc Ser A 153:349–362

    Article  Google Scholar 

  • Diggle P, Rowlingson B (1994) A conditional approach to point process modelling of elevated risk. J R Stat Soc Ser A 157:433–440

    Article  Google Scholar 

  • Diggle P, Gatrell A, Lovett A (1990) Modelling the prevalence of cancer of the larynx in part of Lancashire: a new methodology for spatial epidemiology. In: Thomas RW (ed) Spatial epidemiology. Wiley, New York

    Google Scholar 

  • Dwass M (1957) Modified randomization tests for nonparametric hypotheses. Ann Math Stat 28:181–187

    Article  MathSciNet  MATH  Google Scholar 

  • Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer, New York

    Book  MATH  Google Scholar 

  • Haining R (2003) Spatial data analysis: theory and practice. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Huang L, Kulldorff M, Gregorio D (2007) A spatial scan statistic for survival data. Biometrics 63:109–118

    Article  MathSciNet  MATH  Google Scholar 

  • Jung I, Cho H (2015) A nonparametric spatial scan statistic for continuous data. Int J Health Geogr 14:30

    Article  Google Scholar 

  • Kelsall J, Diggle P (1995) Non-parametric estimation of spatial variation in relative risk. Stat Med 14:2335–2342

    Article  Google Scholar 

  • Klassen A, Kulldorff M, Curriero F (2005) Geographical clustering of prostate cancer grade and stage at diagnosis, before and after adjustment for risk factors. Int J Health Geogr 4:1

    Article  Google Scholar 

  • Kulldorff M (1997) A spatial scan statistic. Commun Stat Theory Methods 26:1481–1496

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff M, Huang L, Konty K (2009) A scan statistic for continuous data based on the normal probability model. Int J Health Geogr 8:58

    Article  Google Scholar 

  • Lawson A, Denison D (2002) Spatial cluster modelling. Chapman and Hall/CRC, London

    Book  MATH  Google Scholar 

  • Loh J, Zhu Z (2007) Accounting for spatial correlation in the scan statistic. Ann Appl Stat 1: 560–584

    Article  MathSciNet  MATH  Google Scholar 

  • Mann H, Whitney D (1947) On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat 18:50–60

    Article  MathSciNet  MATH  Google Scholar 

  • Nagarwalla N (1996) A scan statistic with a variable window. Stat Med 15:845–850

    Article  Google Scholar 

  • Naus J (1963) Clustering of random points in the line and plane. Ph.D. thesis, Rutgers University, New Brunswick

    Google Scholar 

  • Saporta G (2011) Probabilités, analyse des données et statistique. Technip, Paris

    MATH  Google Scholar 

  • Viel JF, Floret N, Mauny F (2005) Spatial and space-time scan statistics to detect low clusters of sex ratio. Environ Ecol Stat 12:289–299

    Article  MathSciNet  Google Scholar 

  • Wilks S (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat 9:60–62

    Article  MATH  Google Scholar 

  • Zhang T, Zhang Z, Lin G (2012) Spatial scan statistics with overdispersion. Stat Med 31:762–774

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Institut Montpelliérain Alexander Grothendieck, University of Montpellier, Cedex 5, 34 095, Montpellier, France

    Lionel Cucala

Authors
  1. Lionel Cucala
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lionel Cucala .

Editor information

Editors and Affiliations

  1. University of Connecticut Dept. Statistics, Storrs, Connecticut, USA

    Joseph Glaz

  2. University of Pireaus Dept. Statistics & Insurance Sciences, Piraeus, Greece

    Markos V. Koutras

Section Editor information

  1. Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, 06269-4120, Storrs, CT, USA

    Joseph Glaz

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this entry

Cite this entry

Cucala, L. (2017). Variable Window Scan Statistics: Alternatives to Generalized Likelihood Ratio Tests. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_36-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-8414-1_36-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8414-1

  • Online ISBN: 978-1-4614-8414-1

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation