We present a deconvolution estimator for the density function of a random variable from a set of independent replicate measurements. We assume that measurements are made with normally distributed errors having unknown and possibly heterogeneous variances. The estimator generalizes well-known deconvoluting kernel density estimators, with error variances estimated from the replicate observations. We derive expressions for the integrated mean squared error and examine its rate of convergence as n → ∞ and the number of replicates is fixed. We investigate the finite-sample performance of the estimator through a simulation study and an application to real data.

中文翻译：

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具有重复异方差测量的密度估计

我们为来自一组独立重复测量的随机变量的密度函数提供了一个解卷积估计器。我们假设测量是用具有未知和可能异质方差的正态分布误差进行的。估计器概括了众所周知的去卷积核密度估计器，误差方差是从重复观察中估计出来的。我们推导出积分均方误差的表达式，并检查其收敛速度为 n → ∞ 并且重复次数是固定的。我们通过模拟研究和对实际数据的应用来研究估计器的有限样本性能。