Related papers: An alternative to Moran's I for spatial autocorrel…
Moran's index is a basic measure of spatial autocorrelation, which has been applied to varied fields of both natural and social sciences. A good measure should have clear boundary values or critical value. However, for Moran's index, both…
Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer…
A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time…
Spatial autocorrelation coefficients such as Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation…
Comparing spatial data sets is a ubiquitous task in data analysis, however the presence of spatial autocorrelation means that standard estimates of variance will be wrong and tend to over-estimate the statistical significance of…
Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer…
Spatial autocorrelation plays an important role in geographical analysis, however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore,…
Physical or geographic location proves to be an important feature in many data science models, because many diverse natural and social phenomenon have a spatial component. Spatial autocorrelation measures the extent to which locally…
Measuring the degree of spatial spreading of a sample can be of great interest when sampling from a spatial population. The commonly used spatial balance index by Grafstr\"om et al. (2012) is particularly effective in comparing the level of…
Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data…
In statistics, the Durbin-Watson test is always employed to detect the presence of serial correlation of residuals from a least squares regression analysis. However, the Durbin-Watson statistic is only suitable for ordered time or spatial…
The Local Moran's I statistic is a valuable tool for identifying localized patterns of spatial autocorrelation. Understanding these patterns is crucial in spatial analysis, but interpreting the statistic can be difficult. To simplify this…
As a rule statistical measures are often vulnerable to the presence of outliers and spatial correlation coefficients, critical in the assessment of spatial data, remain susceptible to this inherent flaw. In contexts where data originates…
Spatial autocorrelation analysis is the basis for spatial autoregressive modeling. However, the relationships between spatial correlation coefficients and spatial regression models are not yet well clarified. The paper is devoted to explore…
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…
We propose a novel estimation procedure for models with endogenous variables in the presence of spatial correlation based on Eigenvector Spatial Filtering. The procedure, called Moran's $I$ 2-Stage Lasso (Mi-2SL), uses a two-stage Lasso…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…