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Title: Functional regression analysis of distributional data using quantile functions Authors:  Veerabhadran Baladandayuthapani - University of Michigan (United States)
Arvind Rao - The University of Texas MD Anderson Cancer Center (United States)
Jeff Morris - MD Anderson Cancer Center (United States)
Hojin Yang - University of Nevada Reno (United States) [presenting]
Abstract: The aims are to look at the subject specific distribution from observing the large number of repeated measurements for each subject and to determine how a set of covariates effects various aspects of the underlying subject-specific distribution, including the mean, median, variance, skewness, heavy tailedness, and various upper and lower quantiles. To address these, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function. To account for smoothness in the quantile functions, we introduce novel basis functions adapting to the features of a given data set. Then, we build a Bayesian framework that uses nonlinear shrinkage of basis coefficients to regularize the functional regression coefficients and allows fully Bayesian inferences after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and illustrate the method using a biomedical imaging data set in which we relate the distribution of pixel intensities from a tumor image to various demographic, clinical, and genetic characteristics.