Smoothness-Penalized Deconvolution (SPeD) of a Density Estimate
Smoothness-Penalized Deconvolution (SPeD) of a Density Estimate
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DOI：
10.1080/01621459.2023.2259028
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发表时间：
2023-11-08
影响因子：
3.7
通讯作者：
Ruppert，David
中科院分区：
文献类型：
--
作者：
Kent，David;Ruppert，David
本文讨论的反褶积问题估计平方可积的概率密度从观测污染的附加测量误差具有已知的密度。该估计器从受污染观测值的密度估计开始，并最大限度地减少因积分平方导数而受到惩罚的重建误差。反卷积理论主要集中在基于核或小波的技术，但其他方法，包括基于样条的技术和这种平滑惩罚估计已被发现优于核方法在模拟研究。本文通过为平滑惩罚方法建立渐近保证来填补其中的一些空白。一致性建立在平均积分平方误差，并得出高斯，柯西，和拉普拉斯误差密度的收敛速度，达到一些下界已经在文献中。对于大多数结果，假设是弱的;估计量可以与比去卷积核更广泛的误差密度一起使用。我们的应用示例估计了随机采样下某些细菌分离株的平均细胞毒性的密度;这种平均细胞毒性只能通过实验测量，具有加性误差，从而导致去卷积问题。我们还描述了一种方法近似的解决方案，由三次样条，减少到一个二次规划。本文的补充材料可在网上查阅。
This article addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squaredmth derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including spline-based techniques and this smoothness-penalized estimator have been found to outperform kernel methods in simulation studies. This article fills in some of these gaps by establishing asymptotic guarantees for the smoothness-penalized approach. Consistency is established in mean integrated squared error, and rates of convergence are derived for Gaussian, Cauchy, and Laplace error densities, attaining some lower bounds already in the literature. The assumptions are weak for most results; the estimator can be used with a broader class of error densities than the deconvoluting kernel. Our application example estimates the density of the mean cytotoxicity of certain bacterial isolates under random sampling; this mean cytotoxicity can only be measured experimentally with additive error, leading to the deconvolution problem. We also describe a method for approximating the solution by a cubic spline, which reduces to a quadratic program. Supplementary materials for this article are available online.