Spatially clustered varying coefficient model

In various applications with large spatial regions, the relationship between response variable and covariates is expected to exhibit complex patterns. We propose a spatially clustered varying coefficient model, where regression coefficients are allowed vary smoothly within each cluster but change abruptly across boundaries of adjacent clusters, we develop unified approach for simultaneous estimation identification. The approximated by penalized splines, clusters identified through fused concave penalty on differences in neighboring locations, neighbors specified minimum spanning tree (MST). optimization solved efficiently based alternating direction method multipliers, using sparsity structure from MST. Furthermore, establish oracle property proposed considering Numerical studies show that can incorporate neighborhood information automatically detect possible patterns coefficients. An empirical study oceanography illustrates promising provide informative results.