$NA$ 相依样本部分线性模型估计理论

考虑部分线性模型 ,其中误差为NA相依样本,具有公共未知分布函数G(·),卢为未知参数, g(·)为未知函数.本文首先建立β和g(·)的相合性估计βn和gn(·),然后基于βn和gn(·)构造出G(·)的非参数估计Gn(·),最后在适当条件下,建立了Gn(·)一致强相合于G(·).

ESTIMATION THEORY IN PARTLY LINEAR REGRESSION MODELS UNDER $NA$ DEPENDENT SAMPLES

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