Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of an Inverse Spatial Autoregressive Model for Estimating
  Moran's Index   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 product of the size variable. The inner product equation is actually a
spatial autocorrelation model. However, the theoretical basis of the inner
product equation for Moran's index is not clear. This paper is devoted to
revealing the antecedents and consequences of the inner product equation of
Moran's index. The method is mathematical derivation and empirical analysis.
The main results are as follows. First, the inner product equation is derived
from a simple spatial autoregressive model, and thus the relation between
Moran's index and spatial autoregressive coefficient is clarified. Second, the
least squares regression is proved to be one of effective approaches for
estimating Moran's index and spatial autoregressive coefficient. Third, the
value ranges of the Moran's index and spatial autoregressive coefficient can be
identified from three angles of view. A conclusion can be drawn that spatial
autocorrelation model is actually an inverse spatial autoregressive model, and
Moran's index, spatial autoregressive models, and canonical Moran's scatterplot
can be integrated into the same framework through inner product and outer
product equations. This work may be helpful for understanding the connections
and differences between spatial autocorrelation measurements and spatial
autoregressive modeling.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin