A0351
Title: Functional quantile principal component analysis
Authors: Alvaro Mendez-Civieta - Columbia University (United States)
Ying Wei - Columbia University (United States)
Keith Diaz - Columbia University (United States)
Jeff Goldsmith - Columbia University (United States) [presenting]
Abstract: Functional quantile principal component analysis (FQPCA) is introduced, a dimensionality reduction technique that extends the concept of functional principal components analysis (FPCA) to the examination of participant-specific quantile curves. The approach borrows strength across participants to estimate patterns in quantiles, and participant-level data is used to estimate loadings on those patterns. As a result, FQPCA is able to capture shifts in the scale and distribution of data that affect participant-level quantile curves and is also a robust methodology suitable for dealing with outliers, heteroscedastic data or skewed data. The need for such methodology is exemplified by physical activity data collected using wearable devices. Participants often differ in the timing and intensity of physical activity behaviors, and capturing information beyond the participant-level expected value curves produced by FPCA is necessary for robust quantification of diurnal patterns of activity. The methods are illustrated using accelerometer data from the National Health and Nutrition Examination Survey (NHANES) and produce participant-level 10\%, 50\%, and 90\% quantile curves over 24 hours of activity. The proposed methodology is supported by simulation results and is available as an R package.
