Missing Responses At Random In Functional Single Index Model Data For Time Series Data

In the field of functional data analysis(FDA),functional single index model(FSIM)is the current research hotspot.In FDA,the high-dimensional characteristics of functional data make researchers constantly optimize statistical analysis methods,while the dimension of data can be reduced by using single index model,which means it could avoid the "dimension disaster" problem.There are more and more theoretical research and application analysis in FDA.On the other hand,from the point of view of avoiding the difficulty of algorithm landing,we focus on the study of the most common data with the characteristics of missing at random(MAR)and time series in daily production and life.On this basis,the theoretical results of the estimator are given,and the effectiveness of the estimation method is verified by a series of simulation experiments and actual case analysis.The main contents are as follows:(1)Regression estimation of FSIM with responses MARFor the time series data,this paper studies the estimation problem of the random missing function single exponential regression model(FSIRM).More precisely,the uniform almost complete convergence rate(UACCR)and asymptotic normality(AN)of the estimators are obtained respectively under some general conditions.In addition,we simulated the performance of estimator in the case of finite sample.Finally,we use the actual monthly electricity consumption data of the U.S.residential and commercial sectors and sea surface temperature data to illustrate the practicability of the method.(2)Conditional density estimation of FSIM with responses MARIn this part,based on previous research,we study the estimation of the conditional density of the FSIM with responses MAR,and obtain the convergence rate of the estimator.Then,the simulation experiment of the sample performance under the finite dimension of the density estimation is carried out.Finally,real SST data are used to verify the effectiveness of our method.