α-混合相依函数型数据改良核回归估计的渐近正态性

Asymptotic normality of modified kernel regression estimator for α-mixing functional data

文章对回归模型Y=r(X)+ε进行了研究。设{(Xi,Yi),1≤i≤n}为取值于E×R上的一组同分布样本,其中E是由半度量d(.,.)生成的某个抽象的半度量空间,R是一个实数空间。在α-混合相依情形下,利用Bernstein大块小块过程,建立函数型数据的改良核回归估计的渐近正态性。

In this paper, the regression model Y=r（X）＋ε is investigated. { （Xi ,Yi）, 1≤i≤n} is set as the random vectors assumed to be identically distributed values taken in EXR, where E is a certain abstract semi-metric space endowed with a semi-metric d（ · , ·） and R is a real space. The asymptotic normality of a modified kernel regression estimator for α-mixing functional data is established by employing Bernstein＇s big-block and small-block procedure.