References
- Aldstadt, J. and Getis, A., 2006. Using AMOEBA to create a spatial weights matrix and identify spatial clusters. Geographical Analysis, 38 (4), 327–343. doi:https://doi.org/10.1111/j.1538-4632.2006.00689.x
- Anselin, L., 1988. Spatial econometrics: methods and models. Vol. 4. Dordrecht: Springer Science & Business Media.
- Anselin, L., 1995. Local indicators of spatial association—LISA. Geographical Analysis, 27 (2), 93–115. doi:https://doi.org/10.1111/j.1538-4632.1995.tb00338.x
- Anselin, L., 2019. A local indicator of multivariate spatial association: extending Geary’s C. Geographical Analysis, 51 (2), 133–150. doi:https://doi.org/10.1111/gean.12164
- Bandyopadhyay, S., Lahiri, S.N., and Nordman, D.J., 2015. A frequency domain empirical likelihood method for irregularly spaced spatial data. The Annals of Statistics, 43 (2), 519–545. doi:https://doi.org/10.1214/14-AOS1291
- Bauman, D., et al., 2018. Optimizing the choice of a spatial weighting matrix in eigenvector‐based methods. Ecology, 99 (10), 2159–2166. doi:https://doi.org/10.1002/ecy.2469
- Cliff, A. and Ord, K., 1972. Testing for spatial autocorrelation among regression residuals. Geographical Analysis, 4 (3), 267–284. doi:https://doi.org/10.1111/j.1538-4632.1972.tb00475.x
- Cressie, N., 1993. Statistics for spatial data. New York: John Wiley & Sons.
- Deb, S., Pourahmadi, M., and Wu, W.B., 2017. An asymptotic theory for spectral analysis of random fields. Electronic Journal of Statistics, 11 (2), 4297–4322. doi:https://doi.org/10.1214/17-EJS1326
- Delgado, M.A. and Robinson, P.M., 2015. Non-nested testing of spatial correlation. Journal of Econometrics, 187 (1), 385–401. doi:https://doi.org/10.1016/j.jeconom.2015.02.044
- Fauchald, P., Erikstad, K.E., and Skarsfjord, H., 2000. Scale‐dependent predator–prey interactions: the hierarchical spatial distribution of seabirds and prey. Ecology, 81 (3), 773–783.
- Fuentes, M., 2007. Approximate likelihood for large irregularly spaced spatial data. Journal of the American Statistical Association, 102 (477), 321–331. doi:https://doi.org/10.1198/016214506000000852
- Geary, R.C., 1954. The contiguity ratio and statistical mapping. The Incorporated Statistician, 5 (3), 115–146. doi:https://doi.org/10.2307/2986645
- Getis, A., 2009. Spatial weights matrices. Geographical Analysis, 41 (4), 404–410. doi:https://doi.org/10.1111/j.1538-4632.2009.00768.x
- Getis, A. and Aldstadt, J., 2004. Constructing the spatial weights matrix using a local statistic. Geographical Analysis, 36 (2), 90–104. doi:https://doi.org/10.1111/j.1538-4632.2004.tb01127.x
- Getis, A. and Ord, J.K., 1992. The analysis of spatial association by use of distance statistics. Geographical Analysis, 24 (3), 189–206. doi:https://doi.org/10.1111/j.1538-4632.1992.tb00261.x
- Gonzalez, R.C. and Woods, R.E., 2008. Digital image processing. Hoboken, NJ: Prentice Hall.
- Guinness, J., 2019. Spectral density estimation for random fields via periodic embeddings. Biometrika, 106 (2), 267–286. doi:https://doi.org/10.1093/biomet/asz004
- Hay, G.J., et al., 2001. A multiscale framework for landscape analysis: object-specific analysis and upscaling. Landscape Ecology, 16 (6), 471–490. doi:https://doi.org/10.1023/A:1013101931793
- Horn, B., Klaus, B., and Horn, P., 1986. Robot vision. Cambridge, MA: MIT Press.
- Kelejian, H.H. and Prucha, I.R., 2001. On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics, 104 (2), 219–257. doi:https://doi.org/10.1016/S0304-4076(01)00064-1
- Kelejian, H.H. and Robinson, D.P., 1992. Spatial autocorrelation: a new computationally simple test with an application to per capita county police expenditures. Regional Science and Urban Economics, 22 (3), 317–331. doi:https://doi.org/10.1016/0166-0462(92)90032-V
- Lu, G.Y. and Wong, D.W., 2008. An adaptive inverse-distance weighting spatial interpolation technique. Computers & Geosciences, 34 (9), 1044–1055. doi:https://doi.org/10.1016/j.cageo.2007.07.010
- Matsuda, Y. and Yajima, Y., 2009. Fourier analysis of irregularly spaced data on Rd. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71 (1), 191–217. doi:https://doi.org/10.1111/j.1467-9868.2008.00685.x
- Meisel, J.E. and Turner, M.G., 1998. Scale detection in real and artificial landscapes using semivariance analysis. Landscape Ecology, 13 (6), 347–362. doi:https://doi.org/10.1023/A:1008065627847
- Moran, P.A., 1950. Notes on continuous stochastic phenomena. Biometrika, 37 (1/2), 17–23. doi:https://doi.org/10.1093/biomet/37.1-2.17
- Oman, S.D. and Mateu, J., 2019. The latent scale covariogram: a tool for exploring the spatial dependence structure of nonnormal responses. Journal of Computational and Graphical Statistics, 28 (1), 127–141. doi:https://doi.org/10.1080/10618600.2018.1482766
- Ord, J.K. and Getis, A., 1995. Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27 (4), 286–306. doi:https://doi.org/10.1111/j.1538-4632.1995.tb00912.x
- Perraudin, N. and Vandergheynst, P., 2017. Stationary signal processing on graphs. IEEE Transactions on Signal Processing, 65 (13), 3462–3477. doi:https://doi.org/10.1109/TSP.2017.2690388
- Rao, S.S., 2018. Statistical inference for spatial statistics defined in the Fourier domain. The Annals of Statistics, 46 (2), 469–499.
- Rogerson, P.A., 2011. Optimal geographic scales for local spatial statistics. Statistical Methods in Medical Research, 20 (2), 119–129. doi:https://doi.org/10.1177/0962280210369039
- Rogerson, P.A. and Kedron, P., 2012. Optimal weights for focused tests of clustering using the local Moran statistic. Geographical Analysis, 44 (2), 121–133. doi:https://doi.org/10.1111/j.1538-4632.2012.00840.x
- Solomon, C. and Breckon, T., 2011. Fundamentals of digital image processing: a practical approach with examples in Matlab. Hoboken, NJ: John Wiley & Sons.
- Sonka, M., Hlavac, V., and Boyle, R., 2014. Image processing, analysis, and machine vision. Toronto: Nelson Education.
- Ver Hoef, J.M., Cressie, N., and Barry, R.P., 2004. Flexible spatial models for kriging and cokriging using moving averages and the Fast Fourier Transform (FFT). Journal of Computational and Graphical Statistics, 13 (2), 265–282. doi:https://doi.org/10.1198/1061860043498
- Westerholt, R., et al., 2018. A statistical test on the local effects of spatially structured variance. International Journal of Geographical Information Science, 32 (3), 571–600. doi:https://doi.org/10.1080/13658816.2017.1402914
- Westerholt, R., Resch, B., and Zipf, A., 2015. A local scale-sensitive indicator of spatial autocorrelation for assessing high-and low-value clusters in multiscale datasets. International Journal of Geographical Information Science, 29 (5), 868–887. doi:https://doi.org/10.1080/13658816.2014.1002499
- Wiener, N., 1930. Generalized harmonic analysis. Acta Mathematica, 55, 117–258. doi:https://doi.org/10.1007/BF02546511
- Wu, J., et al., 2000. Multiscale analysis of landscape heterogeneity: scale variance and pattern metrics. Geographic Information Sciences, 6 (1), 6–19.
- Wu, Q., et al., 2020. Multi-scale identification of urban landscape structure based on two-dimensional wavelet analysis: the case of metropolitan Beijing, China. Ecological Complexity, 43, 100832. doi:https://doi.org/10.1016/j.ecocom.2020.100832
- Yao, T. and Journel, A.G., 1998. Automatic modeling of (cross) covariance tables using fast Fourier transform. Mathematical Geology, 30 (6), 589–615. doi:https://doi.org/10.1023/A:1022335100486
- Zhang, N. and Zhang, H., 2011. Scale variance analysis coupled with Moran’s I scalogram to identify hierarchy and characteristic scale. International Journal of Geographical Information Science, 25 (9), 1525–1543. doi:https://doi.org/10.1080/13658816.2010.532134