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.
出处
《应用概率统计》
CSCD
北大核心
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
