Recursive Kernel Estimation Of Nonparametric Regression Model With Functional Features

In recent years, with the rapid development of computer and information technology,we often collect a large number of highly intensive data changing continuously overtime, called data with functional feature or functional data. Functional data is seen as asample tracks of continuous time stochastic process valuing in infinite dimensionalfunctional space.Mathematically, such data can be seen as a continuous curve datachanging over time or surface data changing continuously over space. This type data isprevalent in natural science, social science and engineering technology. Furthermore ithas wide application in specific disciplines such as economics, finance, biomedical,environmental meteorology etc. The theory and methods of statistical model based onfunctional data attract many scholars at home and abroad,and become a hot topic in thefield of modern statistical research.In this paper,the author further study on the nonparametric regression model basingon functional data. And we construct a recursive kernel estimation of the unknownnonparametric regression function operator in the model. We generalize the classicalNadaraya-Watson kernel estimator to a family of recursive kernel estimator and extendthe real respond variable to functional respond variable. Using the Kolmogorov’sentropy, the rates of uniform almost complete convergence of the recursive estimatorare obtained for independent identically distributied(i.i.d.) and-mixing dependentfunctional time series data, which extend the related results in the references..