M-估计下误差密度核估计的相合性

Convergence for Kernel Estimation of Error Density in M-Estimator

线性模型Yi=x1iβ+ei,i=1,2,…,其中{ei}i∞=1 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．

Linear lnodel Yi= xi1 β+ ei, i = 1, 2,…, where {ei}i∞=1, 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.