The Exact Distribution of Moran's <i>I</i>

Tiefelsdorf, Michael; Boots, Barry

doi:10.1068/a270985

Cited by 252 publications

(127 citation statements)

References 17 publications

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“…The assumption is of the utmost importance for the maximum-likelihood tests and is very useful in those linked to the Knox statistic. The exact distribution of Moran's test, even assuming normality is not standard and depends on the eigenvalues of the weighting matrix (Tiefelsdorf and Boots, 1995, Tiefelsdorf, 2000, Kelejian and Prucha, 2001. Under relatively weak conditions, this distribution converges to the normal distribution (Sen, 1976).…”

Section: Introductionmentioning

confidence: 99%

A non-parametric spatial independence test using symbolic entropy

Hernández

Matilla-García

Mur

et al. 2010

Regional Science and Urban Economics

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RESUMENIn the present paper, we construct a new, simple, consistent and powerful test for spatial independence, called the SG test, by using symbolic dynamics and symbolic entropy as a measure of spatial dependence. We also give a standard asymptotic distribution of an affine transformation of the symbolic entropy under the null hypothesis of independence in the spatial process. The test statistic and its standard limit distribution, with the proposed symbolization, are invariant to any monotonuous transformation of the data.The test applies to discrete or continuous distributions. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We include a Monte Carlo study of our test, together with the well-known Moran's I, the SBDS (de Graaff

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Section: Introductionmentioning

confidence: 99%

A non-parametric spatial independence test using symbolic entropy

Hernández

Matilla-García

Mur

et al. 2010

Regional Science and Urban Economics

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“…Tiefelsdorf and Boots [18] show that nλ (2) (C)/1 n 'C1 n ≈ λ (2) (C)/λ(C) is approximately the largest possible value of Moran's I. For many of the graphs in M05, there is a large gap between λ(C) and λ (2) (C), but this occurs for none of the 70 configurations.…”

Section: Extreme Eigenvaluesmentioning

confidence: 99%

Some Fast Methods for Fitting Some One-parameter Spatial Models

Martin¹

2005

Journal of Mathematics and Statistics

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It is common in geographic modelling to use a one-parameter spatial model to specify the inverse covariance matrix in terms of I-βW, for some known matrix W. Exact Gaussian maximum likelihood estimation of β requires evaluation of the determinant of the covariance matrix. For large data sets, this evaluation of the determinant can be slow and good approximations can be useful. Seventy regional configurations are used to consider some approximations to the determinant of I-βW that are fast to evaluate, and their usefulness is compared.

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“…, E n ) are the eigenvectors corresponding to the eigenvalues Λ [22]. For being orthogonal and uncorrelated, each eigenvector can portray distinct map patterns with achievable level of spatial autocorrelation for a given geographic landscape [31]. The function relation has been detected between MC value for a mapped eigenvector and its corresponding eigenvalue as follows:…”

Section: Eigenvector Generation Based On Swmmentioning

confidence: 99%

A Segmented Processing Approach of Eigenvector Spatial Filtering Regression for Normalized Difference Vegetation Index in Central China

Yang

Chen

et al. 2018

IJGI

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Abstract:A segmented processing approach of eigenvector spatial filtering (ESF) regression is proposed to detect the relationship between NDVI and its environmental factors like DEM, precipitation, relative humidity, precipitation days, soil organic carbon, and soil base saturation in central China. An optimum size of 32 × 32 is selected through experiments as the basic unit for image segmentation to resolve the large datasets to smaller ones that can be performed in parallel and processed more efficiently. The eigenvectors from the spatial weights matrix (SWM) of each segmented image block are selected as synthetic proxy variables accounting for the spatial effects and aggregated to construct a global ESF regression model. Results show precipitation and humidity are more influential than other factors and spatial autocorrelation plays a vital role in vegetation cover in central China. Despite the increase in model complexity; the parallel ESF regression model performs best across all performance criteria compared to the ordinary least squared linear regression (OLS) and spatial autoregressive (SAR) models. The proposed parallel ESF approach overcomes the computational barrier for large data sets and is very promising in applying spatial regression modeling to a wide range of real world problem solving and forecasting.

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The Exact Distribution of Moran's I

Cited by 252 publications

References 17 publications

A non-parametric spatial independence test using symbolic entropy

A non-parametric spatial independence test using symbolic entropy

Some Fast Methods for Fitting Some One-parameter Spatial Models

A Segmented Processing Approach of Eigenvector Spatial Filtering Regression for Normalized Difference Vegetation Index in Central China

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