A0786
Title: Transformed function on scalar regression for random distributions
Authors: Sanghun Jeong - Changwon National University (Korea, South) [presenting]
Hojin Yang - Pusan National University (Korea, South)
Mihye Ahn - University of Nevada Reno (United States)
Jongwon Kim - Pusan National University (Korea, South)
Abstract: A novel scalar-on-function regression framework is presented for modeling subject-specific random distributions through a transformed functional approach. By applying a log quantile differential transformation to individual quantile functions, distributional data is embedded into a square-integrable functional space, where functional principal component analysis is used to extract key features. Regression is then performed on principal component scores, enabling the estimation of covariate effects in the projected space. These effects are subsequently transformed back to the original distributional domain, allowing for the interpretation and prediction of entire distributions given covariates. A hypothesis testing procedure is also developed for assessing functional predictor significance. Simulation studies and an application to Canadian climate data illustrate the method's ability to capture complex distributional features such as skewness and multimodality more effectively than existing approaches.
