Robust Estimation Of Partial Function Linear Regression Mode

With the rapid development of computing tools and storage technology,many dif-ferent types of data collection and storage methods have made more and more functional data appear in our field of vision,its rich data information and functional characteristics have made this kind of data widely concerned.In functional data analysis,regression analysis is a common analysis method.In the regression analysis of functional data,a large number of basis functions are often used to reduce the dimension of functional data,which may lead to the problems of over fitting and too much calculation.At the same time,the robust estimation method based on exponential square loss function can effectively resist the influence of peak,thick tail,outliers and so on.Therefore,this dissertation proposes a new estimation method for partial functional linear regression models based on the LASSO method and the exponential squared loss function.Firstly,the wavelet basis function is used to expand the functional covariates,and the partial functional linear regression model is simplified to the classical linear re-gression model.Secondly,we use the LASSO method to select the basis function variables,and transform the estimation problem of the functional linear regression model into the selection problem of wavelet basis.Finally,the exponential square loss function with₁penalty is used to obtain the estimate of the slope function for the functional covariates,and the convergence rate of the obtained estimation and prediction error are proved re-spectively under certain conditions.In addition,we also carried out simulation studies and real data analysis,and the results show that the estimation of the proposed has good effectiveness and robustness.