New procedures for data mining and measurement error models with medical imaging applications

In this dissertation we provide analysis strategies for two research areas: spatial-temporal data mining and measurement error problems. Motivated by analyzing data from a "Neuromuscular Electrical Stimulation" experiment we develop an efficient procedure for mining spatial-temporal data which combines the following modern and newly developed components: data segmentation and registration, statistical smoothing mapping for identifying "activated" regions and a semiparametric model for detecting spatial-temporal similarities/trends from "large-p-small-n" data sets. For measurement error problems we provide new density and regression estimators for nonparametric errors-in-variables models. The errors can be either homogeneous or nonhomogeneous. In contrast to most existing procedures our new estimators are stable, easy to compute and do not depend on a Fourier transform. The asymptotics of the new estimators is investigated. Our procedures have the potential to become powerful new tools in the image analysis and other fields.