回归函数改良核估计的收敛速度

回归函数的核估计在通常情况下需要核函数具有有界支撑 ,随机变量Y要求具有l阶矩 ,其中l>1。在核函数改进为包括无界支撑甚至不可积 ,并且去掉了对Y的矩的其它要求的情形下 ,讨论了回归函数改良核估计在完全样本及在删失样本情形下的收敛速度 ,得出了与原来情形同样的结论 ,推广和改进了文献 [1- 2 ]的相应结果

The Convergence Rates of Improveed Kernel Estimators for Regression Function

The kernel function of kernel estimator for regression function is often defined with compact support, the moment of Y is bigger than one. The convergence rate of the improved kernel estimator is discussed under the improved kernel function. The result is also discussed under random censorship. The class of applicable kernels include those having unbounded support and even not integral .The condition of moment of Y is discarded under the improved kernel estimator. The results are wholly the same as usual and generalize the relative results of the paper .