标题： 密度去卷积的效率 显示英文标题

标题： The Efficiency of Density Deconvolution

摘要： 密度去卷积问题涉及从被噪声污染的样本中恢复目标密度函数 \( g \)。从 Le Cam 局部渐近正态性理论的角度来看，我们证明了具有高斯噪声的非参数密度去卷积行为类似于一个可以通过最大似然方法轻松解决的低维参数问题。这一框架使我们能够简单地解释密度去卷积的统计效率，并简洁地描述高斯噪声对我们估计 \( g \) 的能力的影响，同时依赖经典的极大似然理论，而不是通常用于研究密度去卷积的核估计量。 显示英文摘要

摘要： The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution with Gaussian noise behaves similarly to a low-dimensional parametric problem that can easily be solved by maximum likelihood. This framework allows us to give a simple account of the statistical efficiency of density deconvolution and to concisely describe the effect of Gaussian noise on our ability to estimate g, all while relying on classical maximum likelihood theory instead of the kernel estimators typically used to study density deconvolution.