A0861
Title: Quantile based functional principal component analysis
Authors: Alvaro Mendez Civieta - Universidad Carlos III de Madrid (Spain) [presenting]
Jeff Goldsmith - Columbia University (United States)
Ying Wei - Columbia University (United States)
Abstract: The majority of methodologies in Functional Data Analysis FDA treat the curves as smooth functions observed with error and are centred on modelling the expected curves. However, this approach does not consider the within-subject variability and correlation of the data, as an expected value cannot reflect those. The method presented addresses this gap and seeks to capture the within-subject variability by modelling the subject-specific conditional quantiles. This objective assumes treating each subject as a single realization from its own underlying distribution. When this distribution is symmetric and no outliers in the data, the expected value provides very good results. However, in many applications, the distribution is skewed, with changes over the functional domain that are not reflected in the expected value but can be reflected by modelling the conditional quantiles. The functional quantile principal component analysis, FQPCA, is introduced, a dimensionality reduction technique that extends the concept of Functional Principal Components to the quantile regression framework, obtaining a model that can explain the subject-specific quantiles conditional on a set of loading functions. FQPCA can capture shifts in the scale and distribution of the data that may affect the quantiles but may not affect the mean and is also a robust methodology suitable for dealing with outliers, heteroscedastic data, or skewed data.
