Convergence for Kernel Estimation of Error Density in M-Estimator

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.