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A note on the SG(m) test

Author

Listed:
  • Fernando López
  • Mariano Matilla-García
  • Jesús Mur
  • Antonio Páez
  • Manuel Ruiz

Abstract

López et al. (Reg Sci Urban Econ 40(2–3):106–115, 2010 ) introduce a nonparametric test of spatial dependence, called SG(m). The test is claimed to be consistent and asymptotically Chi-square distributed. Elsinger (Reg Sci Urban Econ 43(5):838–840, 2013 ) raises doubts about the two properties. Using a particular counterexample, he shows that the asymptotic distribution of the SG(m) test may be far from the Chi-square family; the property of consistency is also questioned. In this note, the authors want to clarify the properties of the SG(m) test. We argue that the cause of the conflict is in the specification of the symbolization map. The discrepancies can be solved by adjusting some of the definitions made in the original paper. Moreover, we introduce a permutational bootstrapped version of the SG(m) test, which is powerful and robust to the underlying statistical assumptions. This bootstrapped version may be very useful in an applied context. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Fernando López & Mariano Matilla-García & Jesús Mur & Antonio Páez & Manuel Ruiz, 2016. "A note on the SG(m) test," Journal of Geographical Systems, Springer, vol. 18(1), pages 87-96, January.
    • Handle: RePEc:kap:jgeosy:v:18:y:2016:i:1:p:87-96
    DOI: 10.1007/s10109-015-0221-7
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    as
    1. Manuel Ruiz & Fernando López & Antonio Páez, 2010. "Testing for spatial association of qualitative data using symbolic dynamics," Journal of Geographical Systems, Springer, vol. 12(3), pages 281-309, September.
    2. López, Fernando & Matilla-García, Mariano & Mur, Jesús & Marín, Manuel Ruiz, 2010. "A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 106-115, May.
    3. Elsinger, Helmut, 2013. "Comment on: A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 838-840.
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    More about this item

    Keywords

    SG(m) test; Spatial dependence; Nonparametric tests; Symbolic dynamics; Entropy; Bootstrap; C4;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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