$M$-estimation and deconvolution in a diffusion model with application to biosensor transdermal blood alcohol monitoring

Abstract

With the goal of well-founded statistical inference on an individual's blood alcohol level based on noisy measurements of their skin alcohol content, we develop Mestimation methodology in a general setting. We then apply it to a diffusion equationbased model for the blood/skin alcohol relationship thereby establishing existence, consistency, and asymptotic normality of the nonlinear least squares estimator of the diffusion model's parameter. Simulation studies show agreement between the estimator's performance and its asymptotic distribution, and it is applied to a real skin alcohol data set collected via biosensor.