Estimation And Variable Selection For Function-on-scalar Linear Regression Model

The existing results about regression and variable selection problems in functionon-scalar linear model concerned few about the robustness.However,in practical problems,the above model can be applied in a wide range of scenarios,and there is a demand for the robustness,so in this work,we consider the robust regression and variable selection problems in function-on-scalar linear model.We present two regression methods to solve the presence of outliers in a functionon-scalar data set.The first one based on the group Lasso and the least absolute deviation(LAD)while the second one gives a new penalty function.We also proposed two variable selection methods to select the variables when the dimensions are more than the sample size.One is based on least angle regression(LARS)variable selection method and another method can control the false discovery rate(FDR).All of those methods can deal with categorical variables and continuous variables.Finally,those regression methods are applied to simulate data and a real data set which includes the annual temperature of some Canadian cities and some other variables.We aim at observing the performance of proposed methods on both simulated and real data.The results show that the methods we proposed perform more robust than the traditional method.