z-score of Anselin Local Moran's I

[CanZhang]

Hi!!

On the website ArcGIS Help 10.1 is the formula of z-score of Anselin Local Moran's I. Why are E and E[I2] calculated like that?

Although in "Mitchell, Andy. The ESRI Guide to GIS Analysis, Volume 2. ESRI Press, 2005" has the same formula of E, but there is nothing about E[I2].

Why is the E not the average of neighbor's I even with an exact search radius? Why is V not just the Standard Deviation of neighbor's I?

Attached is the formula of z-score.

[DanPatterson_Retired · Accepted solution]

PLOS ONE: New Approaches for Calculating Moran’s Index of Spatial Autocorrelation 

Nearest Neighbor Analysis

http://geodacenter.asu.edu/system/files/geodaworkbook.pdf

10.2 help ArcGIS Help (10.2, 10.2.1, and 10.2.2) 

additional math link

are some of the few papers that show the alternate expressions of the equation terms, the last one is by Anselin and is used in GeoDa

[CanZhang]

thank you for the references, they are so helpful.

But I didn't find the mathematical processes of E and V.... Why is E=-sum(w)/n-1?? and why is E[I^2] so complicated?

[CanZhang]

I've found it in Anselin 1995. Thank you all the way.