ABSTRACT In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.

中文翻译：

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通过自适应原子反卷积进行细胞计数推断

摘要 在本文中，我们考虑一个称为原子反卷积的统计估计问题。引入可靠性，该模型在考虑流式细胞仪产生的生物数据时具有直接应用。从统计的角度来看，我们的目标是推断表达所选分子的细胞百分比以及与其荧光发射相关的概率分布函数。我们在此提出了一种自适应估计程序，该程序基于 Es、Gugushvili 和 Spreij [(2008), 'Deconvolution for an atomic distribution', Electronic Journal of Statistics, 2, 265–297] 和 Gugushvili, Es 引入的先前反卷积程序，和 Spreij [(2011)，“原子分布的反卷积：收敛率”，非参数统计杂志，23, 1003–1029]。为了自动估计混合参数和混合密度，我们使用 Lepskii 方法，该方法基于使用偏差 - 方差分解的带宽的最佳选择。然后我们推导出一些在 Sobolev 类中被证明是极小极大最优的收敛率（达到一些对数项）。最后，我们将我们的算法应用于模拟和真实的生物数据。