Dimension Reduction for the Conditional Quantiles of Functional Data With Categorical Predictors

Functional data analysis has received significant attention due to its frequent occurrence in modern applications, such as in the medical field, where electrocardiograms or electroencephalograms can be used for a better understanding of various medical conditions. Due to the infinite-dimensional nature of functional elements, the current work focuses on dimension reduction techniques. This study shifts its focus to modeling the conditional quantiles of functional data, noting that existing works are limited to quantitative predictors. Consequently, we introduce the first approach to partial dimension reduction for the conditional quantiles under the presence of both functional and categorical predictors. We present the proposed algorithm and derive the convergence rates of the estimators. Moreover, we demonstrate the finite sample performance of the method using simulation examples and a real dataset based on functional magnetic resonance imaging.