Research On Variable Selection Methods With FDR Control For Spatial Linear Models

The advancement of science and technology has made the collection of data more and more convenient.High-dimensional data generally exists in various fields.Selecting important variables from many variables has become an indispensable step in the process of statistical modeling.For the variable selection of spatial data,previous research only focused on sign consistency or oracle properties,but did not mention the false discovery rate(FDR)of variable selection methods.In this thesis,we develop a variable selection method effectively controling the FDR for spatial linear models.First,the knockoff filtering method is extended to the spatial linear model under the assumption that the error covariance is known.Secondly,for the spatial linear model with conditional autoregressive errors,the construction conditions and numerical solutions of the knockoff variables are proposed,and the penalized maximum likelihood estimator are computed using the local linear approximation and the least angle regression algorithm,giving an effective variable selection procedure to control the FDR.Finally,the validity of the method is verified by numerical simulation and real data analysis.Theoretical analysis and simulation results show that the variable selection method proposed in this thesis can effectively control the FDR while maintaining a high power.This study provides a new method and theoretical support for the variable selection of sptial data analysis.