混合样本下非参数回归模型误差的矩相合估计

On Consistency in Moment of Nonparametric Regression Model Error Density under Mixing Samples

考虑非参数回归模型 Y_i=g(X_i)+ε_i,i=1,2,…,其中误差{ε_i,i≥1)为φ混合随机变量列,且有共同的未知密度 f(x),g(x)=E(Y|X=x)为未知的回归函数,本文由基于 g(x)的非参数估计 (x)定义的残差,然后再由基于残差构造的 f(x)的估计(x),在适当条件下,证明了(x)具有 r(1<r<2)阶平均相合性。

Considered the nonparometric regression model Y_i=g(x_i)+ε_i,where error{ε_i,i≥1} is a(?)- mixing sequence with unknown Common density function f(x),g(x)=E(Y|X=x)is the unknown regression function.In this paper.We define the estimaaates bused on the nonparaaametric estimator g~^_n(x)for g(x),then we construct the estimate f~^_n(x) for f(x)on the basis of the residuals,and obtain its r-thmean consistency un- der suitable condition.