Robust Estimation For Two Kinds Of Functional Models Based On Modal Regression

With the development of science and technology,people's ability to collect information and store information has been improved.At present,in many areas,most of the datasets collected are functional data.For this kind of data analysis,if the function characteristic is ignored,the statistical inference directly by the traditional regression analysis method may lead to the dimension disaster,the fitting,Information loss and other issues.Functional data analysis is a hot topic studied by statistical scholars in recent years.In this paper,we study robust estimation and application for two kinds of functional models based on modal regression,more details are as follows:1.This paper present a robust estimation procedure by using modal regression for partial functional linear regression,which combines common linear model with functional linear regression model.The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions and performs no worse than the least-squares based estimation for normal error case.The slope function is fitted by B-spline.Under suitable conditions,we obtain the convergence rates and asymptotic normality of the estimators.Finally,simulation study and real data example are conducted to examine the finite sample performance of the proposed method.Both the simulation results and biscuit data analysis confirm that the newly proposed method works very well.2.This paper deals with the problem of estimation in single-index partially functional linear regression model based on modal regression,which combines single-index model with functional linear regression model.The functional principal component basis and polynomial splines are employed to estimate the slope function and index function,respectively.Under some mild conditions,the convergence rates of the estimators and mean squared prediction error,and asymptotic normality of parameter vector are obtained.Finally,Finally,we investigate the finite sample performance of the proposed method through a simulation study and the pork data analysis.