非参数回归函数之改良基于分割的估计的强相合性

Strong Convergence of Modified PartitioningEstimates of Nonparametric Regression Functions

摘要: 设(X,Y),(X₁,Y₁),…,(X_n,Y_n)为取值于R^d×R的 i.i.d.随机变量,E(|Y|)＜∞.设m_n(x)为回归函数m(x)=E(Y|X=x)基于分割的估计,本文在对m_n(x)进行改良的条件下得到改良的基于分割的强相合估计。

Abstract: Let (X,Y),(X₁,Y₁),…,(X_n,Y_n) be i.i.d. random vectors taking values inR^d×R withE(|Y|) ＜∞. Let m_n(x) be the partitioning estimate of the regression function m（x）=E(Y|X=x), In this paper, the strongconvetgence of modified partitioning estimate \widehatm_n（x） is shown.