For the semiparametric regression model: \(Y^{(j)}(x_{in},t_{in})=t_{in}\beta+g(x_{in})+e^{(j)}(x_{in})\), 1 ≤ j ≤ k, 1≤ i ≤ n, where t_in ∈ ℝ and x_in ∈ ℝ^p are known to be nonrandom, g is an unknown continuous function on a compact set A in ℝ^p, e^j(x_in) are m-extended negatively dependent random errors with mean zero, Y^(j)(x_in, t_in) represent the j-th response variables which are observable at points x_in, t_in. In this paper, we study the strong consistency, complete consistency and r-th (r > 1) mean consistency for the estimators β_k,n and g_k,n of β and g, respectively. The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables, negatively associated random variables and other mixing random variables. Moreover, we carry out a numerical simulation for our main results.

对于半参数回归模型：\（Y ^ {（j）}（x_ {in}，t_ {in}）= t_ {in} \ beta + g（x_ {in}）+ e ^ {（j）}（ X_ {IN}）\），1≤ Ĵ ≤ ķ，1≤我≤ ñ，其中吨_在∈ℝ和X_在∈ℝ ^p是已知的非随机，克是一个紧凑的集合的未知连续函数甲在ℝ ^p，e ^j（x _in）是m扩展的负相关的随机误差，均值为零，Y ^（j）（x _in，t _in）表示在点x _in，t _in上可观察到的第j个响应变量。在本文中，我们研究了强一致性，完全的一致性和- [R个（[R > 1）的估计量平均一致性β _K，N和克_K，N的β和克分别。本文获得的结果显着改善并扩展了独立随机变量，负相关随机变量和其他混合随机变量的对应变量。此外，我们对主要结果进行了数值模拟。