Functional Nonparametric Data Analysis And There Applications

In recent years,functional data analysis(FDA) has become one of the fields which are experiencing the rapid development.From a conceptual point of view, functional data can be considered as sample-paths of a time-continuous stochastic process whose graphic representation is a set of curves defined on the parameter space of the process.A lot of statisticians worked at extending multivariate techniques from vectors to curves and yielded substantial results.In China,functional data analysis is getting started recently.Meanwhile,almost all research work has been doing in the field of parametric method.In fact,there are a lot of difficulties in the analysis of functional data by parametric method,because the objects of FDA have complex structures and we cannot have a clear knowledge of the data distributions.In some situations,parametric methods fail to give the fight results,so we should extend nonparametric method from vectors to curves.This dissertation is devoted to marry the advantages of free-modeling together with fully functional methodology in order to analyze data with complex structures.The main innovations are listed as follows.Firstly,this dissertation extended the concept of local smoothing from the finite dimensional case to the functional data case by building different semi-metrics. Through reducing dimensions of data,we could analysis the infinite dimensional data in the finite dimensional space.On this basis,moreover,this dissertation extended the kernel regression method to the functional data analysis.Secondly,this dissertation used functional nonparametric statistical approach for the prediction problem.For time series,we rebuilt the data constructions and in such a way that the prediction problem of time series turns to be a standard regression problem of a real valued response given some p-dimensional explanatory variable. Based on The U.S.Industrial Production Index dataset,consist of 1980-2007 monthly data,we conducted the functional nonparametric prediction and the method completed the analysis task efficiently. Finally,this dissertation introduced the nonparametric unsupervised clustering method and used this method to analyze the biological data.The result turned out to be very well.