NA相依样本的非参数核估计

假设非参数衰退模型Yi=g(Xi)+iε,其中残差{iε}是一个具有未知公共密度函数f(x)的NA相依样本,g(x)=E(Y+X=x)是未知衰退函数.今首先在残差基础上定义了非参数估计gn(x)和^fn(x),并在适当条件下证明了gn(x)和^fn(x)分别是g(x)和f(x)的强一致相合估计,同时给出了相应的收敛速度.

The nonparametric kernel estimation under NA dependent samples

We consider the nonparametric regression model Yi=g(Xi)+εi,where the residual {εi} is a NA dependent with unknown common density function f(x),and g(x)=E(Y|X=x) is the unknown regression function.First we define the residual estimates based on the nonparametric estimator gn(x) for g(x),then we construct the estimator f^n(x) for f(x) on the basis of the residuals.The uniform strong convergence rate is established under suitable conditions.