2022/09/18 by Yanguang Chen, Chen, Yanguang
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Physics and Society (physics.soc-ph) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2209.08562
openalex publication_date 2022/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 boundary values and critical value are controversial. In this paper, a novel method is proposed to derive the boundary values of Moran's index. The key lies in finding conditional extremum based on quadratic form of defining Moran's index. As a result, two sets of boundary values are derived naturally for Moran's index. One is determined by the eigenvalues of spatial weight matrix, and the other is determined by the quadratic form of spatial autocorrelation coefficient (-1