Studying The Variable Selection With FDR Control In Functional Data

With the development of science and technology,functional data is common and often appears in many fields.Multivariate functional linear regression problem is a generalization of multivariate linear regression problem under functional data.For the problem of variable selection in scalar condition,people generally define the feature of non-zero regression coefficient as significant feature,while for functional feature,the feature of non-zero regression coefficient function is defined as significant functional feature.For the selection of functional variables,most of the existing methods do not consider the FDR control of functional variables.For the selection procedure of functional variables,statisticians hope to select as many functional features related to response variables as possible under the premise of controlling FDR.In recent years,statisticians have proposed a new method to control FDR by constructing symmetric statistics of non-significant features.Based on this kind of FDR control method,this thesis studies the extension of this kind of method in the case of functional data,and proposes two FDR controling methods for the selection process of functional variables,which are called F-knockoff filter and F-gaussian mirror,respectively.At the same time,we carry out numerical simulations and real data analysis for the two methods,and the results show that the proposed methods can successfully control the FDR of the functional variable selection procedure.