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A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic


  • Min Xu


  • Chang-Lin Mei


  • Na Yan



Recently, Ord and Getis (Ann Reg Sci 48:529–539, 2012 ) developed a local statistic $$H_i$$ H i , called local spatial heteroscedasticity statistic, to identify boundaries of clusters and to describe the nature of heteroscedasticity within clusters. Furthermore, in order to implement the hypothesis testing, Ord and Getis suggested a chi-square approximation method to approximate the null distribution of $$H_i$$ H i , but they said that the validity of the chi-square approximation remains to be investigated and some other approximation methods are still worthy of being developed. Motivated by this suggestion, we propose in this paper a bootstrap procedure to approximate the null distribution of $$H_i$$ H i and conduct some simulation to empirically assess the validity of the bootstrap and chi-square methods. The results demonstrate that the bootstrap method can provide a more accurate approximation than the chi-square method at the cost of more computation time. Moreover, the power of $$H_i$$ H i in identifying boundaries of clusters is empirically examined using the proposed bootstrap method to compute $$p$$ p values of the tests, and the multiple comparison issue is also discussed. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Min Xu & Chang-Lin Mei & Na Yan, 2014. "A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 697-710, May.
  • Handle: RePEc:spr:anresc:v:52:y:2014:i:3:p:697-710
    DOI: 10.1007/s00168-014-0605-5

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    References listed on IDEAS

    1. Bivand, Roger & Müller, Werner G. & Reder, Markus, 2009. "Power calculations for global and local Moran's," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2859-2872, June.
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    More about this item


    C21; C15; C46;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions


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