Some Study On Variable Selection Of Partial Functional Linear Expectile Regression Model

Functional data widely exists in various fields,such as biomedicine,finance and engineering.Modeling and analyzing functional data is useful to study the relationship of the data and make statistical inference.Partial functional linear model is a class of useful model in practice,which contains several scalar predictable variables,one functional predictive variable and a scalar response variable.In real data analysis,there usually exists both functional and scalar predictive variables.Partial functional linear regression model is a powerful tool to deal with such situations.In recent years,expectile regression has been widely investigated and adopted in practice by researchers.Expectile regression is the extension quantile regression method and can be used as a supplement to the quantile regression method.Given predictive variables,they can provide a more complete feature of the conditional distribution of response variables.It is necessary to perform variable selection while practicing expectile regression.Variable selection can identify significant predictive variables effectively and improve the interpretation ability of the models,thus it enjoys a wide range of applications in real data analysis.Variable selection estimation methods with compressive penalties can carry out parameter estimation and variable selection simultaneously.Meanwhile,the resulted estimators possess favorable properties which are welcomed by theoretical and practical researchers.In this paper,we consider the study of variable selection of partial functional linear model via expectile regression.The semi-parametric model is first converted to parametric model by means of functional principal component analysis.Then expectile regression is performed with SCAD or ALasso penalties to obtain the parametric estimators of the selected variables and the slope function estimator.For the parametric estimators,oracle property and asymptotic normality are investigated.The convergence rate is explored for the non-parametric estimator.It can be proved that the existence of scaler variables do not affect the convergence rate of the slope function estimator.Numerical simulations are performed to study the finite sample properties and simulation results show the effectiveness of the proposed method.