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Divergence-based tests of homogeneity for spatial data

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  • Tomáš Hobza
  • Domingo Morales
  • Leandro Pardo

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Tomáš Hobza & Domingo Morales & Leandro Pardo, 2014. "Divergence-based tests of homogeneity for spatial data," Statistical Papers, Springer, vol. 55(4), pages 1059-1077, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:1059-1077
    DOI: 10.1007/s00362-013-0554-6
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    References listed on IDEAS

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    1. Menendez, M. & Morales, D. & Pardo, L. & Vajda, I., 1995. "Divergence-Based Estimation and Testing of Statistical Models of Classification," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 329-354, August.
    2. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
    3. Menendez, M. L. & Pardo, J. A. & Pardo, L. & Zografos, K., 2003. "On tests of homogeneity based on minimum [phi]-divergence estimator with constraints," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 215-234, June.
    4. B Fingleton, 1983. "Independence, Stationarity, Categorical Spatial Data and the Chi-Squared Test," Environment and Planning A, , vol. 15(4), pages 483-499, April.
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    Cited by:

    1. Feng Xu & Zekai He, 2020. "Testing slope homogeneity in panel data models with a multifactor error structure," Statistical Papers, Springer, vol. 61(1), pages 201-224, February.

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