基于<i>M</i>-估计的误差密度估计

基于M-估计的误差密度估计

摘要: 对于线性模型Y_i=x'_iβ十e_i,i=1,2,...,e_i_{i= 1}^∞i.i.d.,e₁有未知密度函数f（x）,本文基于β的M-估计的残差:\widehate_i=Y_i-x_i^\prime \beta, i=1,2, \cdots, n,其中\widehat\beta为β的M-估计,用 \widehatf_n(x)=\frac12 n a_n \sum_i=1^n I\left(x-a_n \leq \widehate_i \leq x+a_n\right)估计f（x）,得到了这种估计的强收敛速度,一致强收敛速度,L₁-模相合性,渐近正态性,重对数律。

Abstract: For linear model Y_i=x'_iβ十e_i,i=1,2,..., the error sequence e_i_{i= 1}^∞i.i.d., e₁ has an unknown density f（x）. In this paper, we estimate f（x） by \widehatf_n(x)=\frac12 n a_n \sum_i=1^n I\left(x-a_n \leq \widehate_i \leq x+a_n\right) and obtain the strong convergence rate, the strong uniform convergence rate, L₁-norm consistency asymptotic normality, law of iterated logarithm.181