固定设计下半参数回归模型参数估计的收敛速度

The Convergence Rate of Estimation for Parameter in a Semi-Parametric Model under Fixed Design

摘要: 考虑固定设计下的半参数回归模型：y_i=x_iβ＋g（t_i）＋e_i，i=1，…，n。其中e_i为随机误差，且Ee₁=0，Ee₁²=σ²＞0，对利用通常采用的非参数权函数法结合最小二乘法得到的参数β和σ²的估计量\widehat\beta_n和\widehat\sigma_n^2，本文在适当条件下得到了\widehat\beta_n和\widehat\sigma_n^2的精确的收敛速度-重对数律。

Abstract: We consider semiparametric regression model under fixed design y_i=x_iβ＋g（t_i）＋e_i，i=1，…，nWhere e_i are random errors with Ee₁=0，Ee₁²=σ²＞0. For the estimators \widehat\beta_n,\widehat\sigma_n^2of β,σ²by nonparametric weight function and least squared method, we establish their accurate convergence rate. i.e., Law of the iterated logarithm.