STRONG CONSISTENCY OF ESTIMATORS IN PARTIAL LINEAR MODEL UNDER NA SAMPLES
NA样本部分线性模型估计的强相合性

Consider the heteroscedastic regression model:$Y^{(j)}(x_{\rm in},t_{\rm in})=t_{\rm in}\beta+g(x_{\rm in})+\sigma_{\rm in}e^{(j)}(x_{\rm in}), 1\leq j\leq m, 1\leq i\leq n$, where $\sigma_{\rm in}^{2}=f(u_{\rm in})$, $(x_{\rm in},t_{\rm in},u_{\rm in})$ are fixed design points, $\beta$ is an unknown parameter, $g(\cdot)$ and $f(\cdot)$ are unknown functions, and the errors $\{e^{(j)}(x_{\rm in})\}$ are mean zero NA random variables. The strong consistency for least-squares estimator and weighted least-squares estimator of $\beta$ is studied based on the family of nonparametric estimates of $g(\cdot)$ and $f(\cdot)$.