The density of various proteins throughout the human brain can be studied through the use of positron emission tomography (PET) imaging. We report here on data from a study of serotonin transporter (5-HTT) binding. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, in this study, primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract and also to determine how such patterns differ between control subjects and depressed patients. Due to the nature of our data, we utilize function-on-scalar regression modeling to make optimal use of our data. Inference on both main effects (position along the tract; diagnostic group) and their interactions is made using permutation testing strategies that do not require distributional assumptions. Also, to investigate the question of homogeneity we implement a permutation testing strategy, which adapts a "block bootstrapping" approach from time series analysis to the functional data setting.
Keywords: Block bootstrap; Functional ANOVA; Functional data; Homogeneity; Permutation testing.