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

考虑固定设计下的半参数回归模型：yi=xiβ＋g（ti）＋ei，i=1，…，n．其中{ei}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的估计量和，本文在适当条件下得到了和的精确的收敛速度-重对数律．

We consider semiparametric regression model under fixed design yi = xiβ + g(ti) + eii = 1, 2,…,n. Where {ei} are random errors with Ee1 = 0, Ee12= σ2. For the estimators ,.of β.σby nonparametric weight function and least squared method, we establish their accurate convergence rate. i.e., Law of the iterated logarithm