Study On Variable Selection In Functional Linear Regression Models

As most widely applied functional data analysis method,functional linear regression models express the discrete observations of the predictor as a smooth function,then statistical inference can be made about a response variable based on the functional data.When there are multiple functional predictors in the model,in order to improve the model's interpretability and forecasting ability,we often want to select the functional predictors which have a significant influence on the response variable.This paper puts forward a new variable selection method in functional linear regression models.First of all,through a base approximation method,functional linear regression models will turn into a general linear regression model,then through correlation learning and penalized least squares or penalized likelihood methods to achieve the selection of important variables.Under some conditions,this method possesses sure screening property and model selection consistency.The proposed variable selection method not only applies to the low-dimensional situation,but also applies to high-dimensional situation.This paper is divided into five parts.The first chapter is the introduction part,mainly introduces the background of the research problem and the present research status,at the same time explain the works have been done.The second chapter will introduce several typical variable selection methods in function linear regression models.The third chapter will introduce a variable selection method based on correlation learning in function linear regression models,and establish the sure screening property and model selection consistency of the proposed method,in addition to introduce a iterative algorithm for variable selection.The fourth chapter will verify the feasibility of the proposed method through the simulated data and empirical data.The fifth chapter will summarize the contents of this paper,at the same time looking forward the future research directions.