Detailed activity assessment using participant-level daily quantile trajectories

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This paper introduces the functional quantile principal component analysis (FQPCA), 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 principal component functions. FQPCA is able to capture shifts on 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. The need for such methodology is exemplified by our motivating example: using the accelerometer data from the National Health and Nutrition Examination Survey (NHANES) we analyze the physical activity level of over $3600$ people during one day. The proposed methodology can deal with sparse and irregular time measurements, is evaluated in synthetic data and real data analyses, and is available as a package in R programming language.