Asymptotic Normality Of Nonparametric Robust Estimator For Spatial Functional Data

With the continuous advancement of technology and theory， the datacollected by people have been showing more and more functional. In thestatistician community it is commonly called ‘functional data’. The functional datais widely used in psychology, biology, economics and meteorology etc. It refers toa continuous changing data such as Space continuous changing data. A commonway to deal with spatial data is the classic space block segmentation method.Nonparametric estimation has little require on statistical model and can use thegeneral information of the data. While the method of kernel estimation is the coreof the regression of nonparametric estimation, but it doesn’t have a certain degreeof interference immunity. Robust estimation is proposed to solve the poor anti-interference of traditional kernel estimation. In summary, the robust estimation ofregression function of spatial functional data has a wide range of research value.Therefore, this discussion of the spatial functional data has a certain practicalsignificance.Specifically, the work in this paper is mainly focused on the nonparametricrobust estimation of regression function based on spatial functional data. First ofall, we mainly introduce the nonparametric regression model of spatial functionaldata. Besides this, under certain assumptions, the robust estimation of theregression variables of the nonparametric spatial functional data is been studiedand its asymptotic normality has been obtained. Then, the approximate1confidence interval of robust estimation function is given based on the former part.