The Estimation Of Conditional Mode Of Functional Single Index Model Under Random Censorship

Condition density plays an important role;not only in exploring relationships between responses and covariates,but also in financial econometrics,The research on conditional density and conditional mode is of great interest.A vast variety of papers use the estimators of conditional density as building blocks.With the emergence of functional data,functional data analysis(FDA)has gradually become a hot topic.In real life,we often get data in different forms.The current data research is not satisfied with completely independent data,but tend to interdependent random censoring and random missing data.Such research results are of practical value.For the dimension processing of high-dimensional data,the single function index model has been widely concerned in recent years.It can reduce the dimension without affecting the characteristics of high-dimensional data.Based on the single function index model,this paper mainly studies the asymptotic properties of conditional density and conditional mode under the condition of random censoring of response variables.The main contents are as follows:First,the uniform almost complete convergence rate of conditional mode estimation of functional single index model under random censorship.Based on the single function index model,a conditional density estimator of the model is constructed,and the almost uniform convergence rates of conditional density and conditional mode for ?-mixed function data with random censored response variables are studied.In addition,a simulation study is used to illustrate the properties of conditional mode estimation,and 200 MB equatorial zonal wind index data is used to verify the effectiveness of the model estimation.Second,the asymptotic normal distribution of conditional mode estimation of functional single index model under random censorship.Based on the first part,we study the asymptotic normal distribution of conditional density and conditional mode estimators for ?-mixed function data with random censored response variables.Finally,the superiority of conditional mode estimation of single function index model is also illustrated by simulation.