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

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.