Title: Resampling methods for high-dimensional data and nonparametric regression with applications to brain imaging, bioinformatics, and sleep/circadian medicine
Description: This work investigates resampling methods for high-dimensional data and nonparametric regression. Chapter 1 proposes null-transform-bootstrap procedures for one- and two-sample problems that provide control of a general type 1 error rate using orthogonal decomposition of a multivariate distribution function into the marginal distributions and the dependence structure (copula). Chapter 2 builds nonparametric model for the effects of homeostatic sleep drive, circadian phase and wake period on human neurobehavioral performance. I investigate empirically how to provide additional regularization to avoid effect of piecewise collinearity of covariate processes. Chapter 3 proposes unified approach for using permutation tests in nonparametric regression. I prove asymptotic exactness of the permutation tests and illustrate the approach using sleep study of chapter 2 to test for the lack of effect and the presence of inter-individual variability.