On Image Response Regression With High-Dimensional Data

A recent issue in statistical analysis is modelling data when the effect variable changes at different locations. This can be difficult to accomplish when the dimensions of the covariates are very high, and when the domain of the varying coefficient functions of predictors are not necessarily regular. This research paper will investigate a method to overcome these challenges by approximating the varying coefficient functions using bivariate splines. We do this by splitting the domain of the varying coefficient functions into a number of triangles, and build the bivariate spline functions based on this triangulation. This major paper will outline detailed theoretical results of this method, and provide simulation studies to demonstrate the efficiency of this approach. Finally, to illustrate the application of this method, we analyze heart disease dataset where the given covariates are in spatially varying form