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Statistical Papers

, Volume 55, Issue 4, pp 1059–1077 | Cite as

Divergence-based tests of homogeneity for spatial data

  • Tomáš HobzaEmail author
  • Domingo Morales
  • Leandro Pardo
Regular Article

Abstract

The problem of testing homogeneity in contingency tables when the data are spatially correlated is considered. We derive statistics defined as divergences between unrestricted and restricted estimated joint cell probabilities and we show that they are asymptotically distributed as linear combinations of chi-square random variables under the null hypothesis of homogeneity. Monte Carlo simulation experiments are carried out to investigate the behavior of the new divergence test statistics and to make comparisons with the statistics that do not take into account the spatial correlation. We show that some of the introduced divergence test statistics have a significantly better behavior than the classical chi-square test for the problem under consideration when we compare them on the basis of the simulated sizes and powers.

Keywords

Test of homogeneity Divergence statistics Chi-square statistic Spatial data 

Notes

Acknowledgments

The authors thank the referees for careful reading of the paper and many interesting improvements. Supported by the Grants MTM2012-37077-C02-01, MTM2012-33740 and SGS12/197/OHK4/3T/14.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsCzech Technical University in PraguePrague 2Czech Republic
  2. 2.Operations Research CenterMiguel Hernández University of ElcheElcheSpain
  3. 3.Department of Statistics and Operations ResearchComplutense University of MadridMadridSpain

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