考虑部分线性模型 $Y_{n,i}=x_{n,i}\beta +g(t_{n,i})+{\epsilon }_{n,i},i=1,\cdots ,n$, 其中误差 $\{{\epsilon }_{n,i}:i=1,\cdots ,n\}$ 为$NA$ 相依 样本, 具有公共未知分布函数 $G(\cdot )$, $\beta$为未知参数, $g(\cdot )$ 为未知函数. 本文首先建立 $\beta$ 和$g(\cdot )$的相合性估计 ${\beta }_n$ 和 ${\tilde{g}}_n(\cdot )$, 然后基于${\beta }_n$ 和 ${\tilde{g}}_n(\cdot )$ 构造出 $G(\cdot )$的非参数估计${\tilde{G}}_n(\cdot )$, 最后在适当条件下, 建立了${\tilde{G}}_n(\cdot )$一致强相合于$G(\cdot )$.

Consider the partly linear regression model: $Y_{in,}=x_{n,i}\beta +g(t_{n,i})+{\epsilon }_{n,i},i=1,\cdots ,n$, where the residual $\{{\epsilon }_{n,i}\}$ is an $NA$ dependent with unknown common distribution function $G(x)$. In this paper, frist we define the residual estimates based on the non-parametric estimator ${\tilde{G}}_n(x)$ and ${\beta }_n$ for $g(x)$ and $\beta$, then we construct the estimate ${\tilde{G}}_n(x)$ for $G(x)$ on the basis of the residuals. The uniform strong consistency are obtained under suitable conditions.