密度泛函核估计的Bootstrap逼近

BOOTSTRAP KERNEL ESTIMATORS FOR DENSITY FUNCTIONALS

设Ｘ１，…，Ｘｎ是从分布密度函数为ｆ的总体中抽取的ｉｄ样本，μ＝ＥＸ１°本文研究了密度泛函θ＝ｆ（μ）的核型估计ｆｎ（ｘ）（其ｘ＝１ｎ∑ｎｉ＝１Ｘｎ，ｆｎ（ｘ）为通常的Ｒｏｓｅｎｂｌａｔ－Ｐａｒｚｅｎ核估计，Ｂｏｏｔｓｔｒａｐ逼近问题．

Let X 1,…,X n be independent identically distributed random variable series, having the common probability density function, with μ=EX 1. In this paper, we discuss the Bootstrap method for the kernel estimation f n(x) of the density functional θ=f(μ) (where x=1n ∑ n i=1 X n,f n(x) is a Resenblatt Parzen kernel estimator).