相依样本下回归函数分割估计的渐近正态性

Asymptotic Normality of Partitioning Estimatior of Regression Function under Dependence Sample

在一种相依样本下,利用鞅的理论证明了回归函数基于分割的估计■渐近正态性,其中I_A(x)为集合A的示性函数。给出了相关定理:在一定的假设条件下,X_i具有密度函数f(x),E|Y|^(2+δ)<∞,EV^(2+δ)(X)<∞,x∈R^d为固定点,nv_N^2→∞。

Under a kind of dependence sample, partitioning estimation of regression function ma（x）=∑i=1^n IAn（x）（Xi）Yi/∑i=1^n IAn（x）（Xi）,is proved with the theory of martingale, where IA （x） is the asymptotic normality of the indicator of set A. A theorem is given that on some conditions, Xi has a density functionf（x）,E｜Y｜^2＋δ 〈∞,EV^2＋δ〈∞,x∈R^d is fixed point, nvn^2→∞, then √nvn（m4x（x）-m（x））→L N（0,σ^2）,n→∞.