<i>M</i>-估计下误差密度核估计的相合性

M-估计下误差密度核估计的相合性

详细信息

1. Chinese People's Armed Police Force Academy, Langfang, 065000;
2. Department of Statistics and Finance of University of Science and Technology of China, Hefei, 230026

摘要: 线性模型Y_i=$x_i^{\prime} \beta+e_i$,i=1,2,…,其中$\left\{e_i\right\}_{i=1}^{\infty}$ i.i.d.有未知密度 f(x)．本文讨论了在对β作一般M－估计后,基于残差做出的误差密度核估计的相合性．在比文献弱的条件下,证明了误差密度核估计的逐点弱相合、逐点强相合和一致强相合。
- M-估计 /
- 残差 /
- 核估计 /
- 相合性
Abstract: Linear lnodelY_i=$x_i^{\prime} \beta+e_i$,i=1,2,…, where$\left\{e_i\right\}_{i=1}^{\infty}$ i.i.d. with unknown density f（x）. In this paper, weconsider some converegence of kernel estimation of error density based on the residuals of M-estimation. Underweaker assumptions than references, the article proves the weak local convergence, the strong loca1 convergence and the strong uniform convergence of kernel estimation of error density.