发表机构
University of Chieti-Pescara; University of Luxembourg（基耶蒂-佩斯卡拉大学; 卢森堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对密度反卷积的不适定问题，提出两阶段基于似然的方法，建立高斯误差下的收敛速率，数值实验及弗雷明汉血压数据应用验证其互补的有限样本表现。
AI 中文摘要
密度反卷积是一个不适定的逆问题，因为恢复潜在分布会放大观测数据中的高频噪声。我们提出一种两阶段基于似然的方法：第一个估计量在正则化高斯混合筛上最大化卷积似然，第二个将拟合的密度作为经验先验，对观测值上得到的条件潜在密度取平均。在模型误设下，两个估计量具有不同的总体目标：后验重构在可识别卷积下局部压缩误设偏差，但在正确的有限维设定下引入额外的一阶方差分量。我们在高斯误差下建立了观测域和潜在域的收敛速率，在普通光滑误差下，直接估计量在L²空间、后验重构在L¹空间达到经典反卷积指数，仅差对数因子。数值实验及对弗雷明汉血压数据的应用表明了它们互补的有限样本表现。
英文摘要
Density deconvolution is an ill-posed inverse problem because recovering the latent density amplifies high-frequency variation in the observed data. We propose a two-stage likelihood procedure. The first estimator maximizes the convolution likelihood over a regularized Gaussian-mixture sieve; the second treats this fit as an empirical prior and averages the fitted conditional latent densities. Under fixed-model misspecification, the estimators generally have different population targets. For bounded local multiplicative perturbations of the latent density, the population posterior map is locally contractive in chi-square divergence under identifiable convolution. Under correct finite-dimensional specification, however, reconstruction adds a nonnegative first-order variance component. For growing sieves, we separate observed-domain estimation, inverse stability, and posterior empirical variation. We derive explicit rates under Gaussian error and recover the classical ordinary-smooth exponent, up to logarithmic factors, with a constructive verification for Laplace error. Simulations and a Framingham blood-pressure application provide empirical performance evidences.
