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We develop $M$-estimation and deconvolution methodology with the goal ofmaking well-founded statistical inference on an individual's blood alcohollevel based on noisy measurements of their skin alcohol content. We first applyour results to a nonlinear least squares estimator of the key parameter thatspecifies the blood/skin alcohol relation in a diffusion model, and establishits existence, consistency, and asymptotic normality. To make inference on theunknown underlying blood alchohol curve, we develop a basis space deconvolutionapproach with regulazation, and determine the asymptotic distribution of theerror process, thus allowing us to compute uniform confidence bands on thecurve. Simulation studies show agreement between the performance of our curveestimators and their asymptotic distributions at low noise levels, and we applyour methods to a real skin alcohol data set collected via a transdermalbiosensor.

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