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### 相依函数型数据的局部回归估计的渐近正态性

• 出版日期:2018-06-25 发布日期:2018-06-22

### Asymptotic Normality of Partially Regressive Estimators for Dependent Functional Data

Li Shuangbo

• Online:2018-06-25 Published:2018-06-22

Abstract: Nonparametric statistics is one important aspect of statistical research, in which the kernel estimation and partial polynomial methods are commonly used. It is quite common to use kernel estimation for functional data. In terms of its convergence rate and asymptotic distribution the theoretical conclusions have already made, no matter it is independent or dependent. It is quite rare to use partial polynomial estimation for functional data analysis, because it is always a conundrum to apply functional data to the partial polynomial estimation. The researches by our predecessors require the data used independent with identical distribution, which is contrary to much of the real data. This paper studies the asymptotic normality of partial regressive estimators for dependent functional data. The methodology of kernel function estimation cannot be extended directly to partially regressive estimation, moreover, the dependent structure also brings up some challenges to our research. This paper adopts the Bernstein Block method to convert the dependent issue into asymptotic independent so as to obtain the asymptotic normality of the estimators. In addition, a simulation study is done to further justify the result of asymptotic normality.