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.
翻译:我们开发了美元估算和分流方法,目的是在对一个人的血液酒精含量进行密集测量的基础上,对一个人的血液酒精含量作出有充分根据的统计推断。我们首先将结果应用到一个非线性最小的正方形关键参数的估测器,该参数在扩散模型中指定了血液/皮肤酒精关系,并确立了其存在性、一致性和无症状的正常性。为了对未知的血液藻类曲线进行推断,我们开发了一个基础性空间分解法,同时进行再凝固,并确定了错误过程的无症状分布,从而使我们能够计算曲线上的统一信任带。模拟研究显示,我们曲线估量器的性能及其低噪音水平的无症状分布是一致的,我们将我们的方法应用到通过转基因生物传感器收集的真实的皮肤酒精数据组中。