部分线性模型误差分布估计的重对数律

The Laws of the Iterated Logarithm for Residuals Estimation in Partial Linear Model

摘要: 考虑部分线性模型，其误差是i.i.d.随机变量，具有公共未知分布G．基于残差构造G的非参数光滑估计\widehatG_n。本文建立了\widehatG_n。收敛于G的Chung－Smirnov型上极限和Kolmogorov-Smirnov，Cramer－VonMises型下极限重对数律。

Abstract: We consider the partial linear model y_i = X_i’β+ g（T_i）+e_i, where the residual e_i is i.i.d. with unknown connon distribution function G . In this paper, on the basis of the residuals, one first define the estimators \widehatG_n of the distribution G of error, then we show that Chung,Smirnov,Kolmogorov-Smirnov and Cremer-Von Mises properties hold of \widehatG_n for G.