分布自由的回归函数核估计的收敛速度

The Convergence Rates of Kernel Estimators for the Distribution Free Regression Function

设 (X1,Y1)、(X2 ,Y2 )、…是取值于Rp×R上的随机向量 (X ,Y)的一列i.i.d样本 ,回归函数m(x) =E(Y|X=x)的核估计为mn(x) = ni=1YiK(x -Xihn) / ni =1K(x -Xihn)在不要求X具有密度函数f(x) ,对分布自由 ,即对所有X的分布 μ和在核函数改进为包括无界支撑的 ,甚至不可积的情形下得出了回归函数m(x) =E(Y|X =x)的核估计及在删失情形下的收敛速度。

Suppose that (X 1,Y 1),(X 2,Y 2)...are i.i.d.samples drawn from (X,Y)((X,Y)∈R p×R).The kernel estimator of regression function m(x)=E(Y|X=x)is defined by m (1) n(x)=ni=1Y iK(x-X ih n)/ni=1K(x-X ih n)In this paper the convergence rate of the kernel estimator is obtained under the distribution free regression function.The result is also obtained under random censorship.The class of applicable kernels includes those having unbounded support and even not integral.