相依样本非参数回归模型误差的相合估计  

Consistent Estimation of Residual Density Function in Nonparametric Regression Model Under Dependent Samples

作　　者：秦更生[1] 蒋泽云[1] 

机构地区：[1]四川大学,成都610064

出　　处：《应用概率统计》1995年第4期371-377,共7页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金资助项目

摘　　要：考虑非参数回归模型Y_i=g(X_i)+c_i,i=1,2,…,其中误差㈦)为吵混合随机变量序列且具有公共的未知密度f(·),g(x)=E(Y|X=t)为未知回归函数。本文首先基于g(·)的非参数估计l(x)定义残差,然后基于残差构造f(·)的估计l(x),最后在适当条件下建立l(x)的逐点相合性及一致强相合性。We consider the nonparametric regression model Yi=g(Xi) +ε1, where the residual {εi} is a stationary φ-mixed process with unknown common density function f(x), g(x) = E(Y\X = x) is the unknown regression function. In this paper, first we define the residuals estimates based on the nonparametric estimator gn(x) for g(x), then we construct the estimate fn(x) for f(x) on the basis of the residuals, the pointwise weak and strong consistency as well as the uniform strong consistency of fn(x) are estabilished under some suitable conditions.

关 键 词：相依样本 误差密度估计 相合性 非参数回归模型 

分 类 号：O212.7[理学—概率论与数理统计]