Integrated squared error of kernel-type estimator of distribution function
Integrated squared error of kernel-type estimator of distribution function
复制标题
分布函数核型估计器的积分平方误差
DOI：
10.1007/bf00050707
复制
发表时间：
1992
影响因子：
1
通讯作者：
I. Chu
中科院分区：
文献类型：
--
作者：
S. Shirahata;I. Chu
LetX1,……从密度函数f(x)的分布函数f(x)中抽取一个随机样本，假设我们想要估计x (x)。已经证明核估计器ofF(x)在平均积分平方误差的意义上优于通常的经验分布函数。本文导出了核估计量的积分平方误差，并与经验分布函数的误差进行了比较。结果表明，在平方误差积分的意义上，核估计量的优越性并不一定成立。
LetX1,...,Xnbe a random sample drawn from distribution functionF(x)with density functionf(x)and suppose we want to estimateX(x). It is already shown that kernel estimator ofF(x)is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.