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The Exact Distribution of Moran's I

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  • M Tiefelsdorf
  • B Boots

Abstract

In analogy to the exact distribution of the Durbin—Watson d statistic for serial autocorrelation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c ) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Imhof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran's I for regression residuals will lie. Furthermore, the proposed methodology is flexible enough to investigate related topics such as the characteristics of the exact distribution for distinct spatial structures as well as their different specifications, the exact power function under different spatial autocorrelation levels, and the distribution of Moran's I for nonnormal random variables.

Suggested Citation

  • M Tiefelsdorf & B Boots, 1995. "The Exact Distribution of Moran's I," Environment and Planning A, , vol. 27(6), pages 985-999, June.
    • Handle: RePEc:sae:envira:v:27:y:1995:i:6:p:985-999
    DOI: 10.1068/a270985
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    References listed on IDEAS

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    1. Savin, N Eugene & White, Kenneth J, 1977. "The Durbin-Watson Test for Serial Correlation with Extreme Sample Sizes or Many Regressors," Econometrica, Econometric Society, vol. 45(8), pages 1989-1996, November.
    2. Farebrother, R W, 1980. "The Durbin-Watson Test for Serial Correlation When There Is No Intercept in the Regression," Econometrica, Econometric Society, vol. 48(6), pages 1553-1563, September.
    3. L'Esperance, Wilford L & Chall, Daniel & Taylor, Daniel, 1976. "An Algorithm for Determining the Distribution Function of the Durbin-Watson Test Statistic," Econometrica, Econometric Society, vol. 44(6), pages 1325-1326, November.
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    1. David C. Folch & Sergio J. Rey, 2016. "The centralization index: A measure of local spatial segregation," Papers in Regional Science, Wiley Blackwell, vol. 95(3), pages 555-576, August.
    2. Christoph Grimpe & Roberto Patuelli, 2011. "Regional knowledge production in nanomaterials: a spatial filtering approach," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 46(3), pages 519-541, June.
    3. Mur, Jesús & Trivez, F. Javier, 2000. "Scale Elements In Spatial Autocorrelation Tests," ERSA conference papers ersa00p97, European Regional Science Association.
    4. Nicola Pontarollo & Roberto Ricciuti, 2015. "Railways and the Productivity Gap in Italy: Persistence and Divergence after Unification," CESifo Working Paper Series 5438, CESifo.
    5. 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.
    6. Jos魍ar𨁍ontero-Lorenzo & Beatriz Larraz-Iribas, 2012. "Space-time approach to commercial property prices valuation," Applied Economics, Taylor & Francis Journals, vol. 44(28), pages 3705-3715, October.
    7. Julie Le Gallo, 2000. "Spatial econometrics (1, Spatial autocorrelation) [Econométrie spatiale (1, Autocorrélation spatiale)]," Working Papers hal-01527290, HAL.
    8. René Van der Kruk, 2001. "Economic Impacts of Wetland Amenities A Spatial Econometric Analysis of the Housing Market," ERSA conference papers ersa01p76, European Regional Science Association.
    9. Daniel A. Griffith & Yongwan Chun, 2016. "Evaluating Eigenvector Spatial Filter Corrections for Omitted Georeferenced Variables," Econometrics, MDPI, vol. 4(2), pages 1-12, June.
    10. repec:rim:rimwps:29-08 is not listed on IDEAS
    11. Roberto Patuelli & Andrea Vaona & Christoph Grimpe, 2010. "The German East‐West Divide In Knowledge Production: An Application To Nanomaterial Patenting," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 101(5), pages 568-582, December.
    12. Reinhold Kosfeld & Christian Dreger, 2006. "Thresholds for employment and unemployment: A spatial analysis of German regional labour markets, 1992–2000," Papers in Regional Science, Wiley Blackwell, vol. 85(4), pages 523-542, November.
    13. Wang, Yiyi & Kockelman, Kara M. & Wang, Xiaokun (Cara), 2013. "Understanding spatial filtering for analysis of land use-transport data," Journal of Transport Geography, Elsevier, vol. 31(C), pages 123-131.
    14. LE GALLO, Julie, 2000. "Econométrie spatiale 1 -Autocorrélation spatiale," LATEC - Document de travail - Economie (1991-2003) 2000-05, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
    15. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    16. Moniruzzaman, Md & Páez, Antonio, 2012. "Accessibility to transit, by transit, and mode share: application of a logistic model with spatial filters," Journal of Transport Geography, Elsevier, vol. 24(C), pages 198-205.

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