论文标题
$ m $ - 估计和反卷积在扩散模型中，并应用于生物传感器透皮血液酒精监测
$M$-estimation and deconvolution in a diffusion model with application to biosensor transdermal blood alcohol monitoring
论文作者
论文摘要
我们开发了$ M $估计和反卷积方法，目的是基于对皮肤酒精含量的嘈杂测量，对个人的血液酒精水平进行了良好的统计推断。我们首先将结果应用于指定扩散模型中血液/皮肤酒精关系的关键参数的非线性最小二乘估计器，并确定其存在，一致性和渐近正态性。为了推断未知的基础血藻曲线，我们通过调节开发了基础空间反卷积方法，并确定误差过程的渐近分布，从而使我们能够在曲线上计算统一的置信带。仿真研究表明，我们的曲线估计器的性能与其渐近分布在低噪声水平之间的一致性，我们将方法应用于通过经透皮生物传感器收集的真实皮肤酒精数据集。
We develop $M$-estimation and deconvolution methodology with the goal of making well-founded statistical inference on an individual's blood alcohol level based on noisy measurements of their skin alcohol content. We first apply our results to a nonlinear least squares estimator of the key parameter that specifies the blood/skin alcohol relation in a diffusion model, and establish its existence, consistency, and asymptotic normality. To make inference on the unknown underlying blood alchohol curve, we develop a basis space deconvolution approach with regulazation, and determine the asymptotic distribution of the error process, thus allowing us to compute uniform confidence bands on the curve. Simulation studies show agreement between the performance of our curve estimators and their asymptotic distributions at low noise levels, and we apply our methods to a real skin alcohol data set collected via a transdermal biosensor.
