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
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摘要: 线性模型Yi=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。Abstract: Linear lnodelYi=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.
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