Deconvolving a density from partially contaminated observations
Deconvolving a density from partially contaminated observations
复制标题
从部分污染的观测值中解卷积密度
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
C. Hesse
中科院分区：
文献类型：
--
作者：
C. Hesse
我们考虑了当密度的独立数据X1，…，Xn被测量误差部分污染时，估计连续有界概率密度函数的问题。具体地说，观测值Y1，…，Yn使得P(Yj=Xj)=p和P(Yj=Xj+[epsilon]j)=1-p，其中误差[epj]j(彼此独立并且与Xj无关)并且与已知分布相同分布。当p=0时，众所周知，通过核密度估计器进行反卷积的收敛速度非常慢。对于正态分布的[epsilon]j，最佳可能的速率是逐点对数级的，并且以均方误差表示。在这篇文章中，我们证明了仅对部分(0
We consider the problem of estimating a continuous bounded probability density function when independent data X1, ..., Xn from the density are partially contaminated by measurement error. In particular, the observations Y1, ..., Yn are such that P(Yj = Xj) = p and P(Yj = Xj + [epsilon]j) = 1 - p, where the errors [epsilon]j are independent (of each other and of the Xj) and identically distributed from a known distribution. When p = 0 it is well known that deconvolution via kernel density estimators suffers from notoriously slow rates of convergence. For normally distributed [epsilon]j the best possible rates are of logarithmic order pointwise and in mean square error. In this paper we demonstrate that for merely partially(0