Local principal differential analysis: Graphical methods for functional data with covariates |
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| Authors: | Joan G Staniswalis Christopher Dodoo Anu Sharma |
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| Institution: | 1. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, USA;2. Department of Biostatistics &3. Epidemiology, Paul L. Foster School of Medicine, Texas Tech University Health Science Center, El Paso, TX, USA;4. Department of Speech, Language and Hearing Sciences, University of Colorado at Boulder, Boulder, CO, USA |
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| Abstract: | We focus on principal differential analysis (PDA) of functional data for obtaining a low-dimensional representation of a collection of curves. PDA assumes there exists a linear differential operator that results in the zero-function when it is applied to each of the data curves, or equivalently, that the curves belong to a low-dimensional subspace of a normed linear space. PDA sets out to estimate this linear differential operator from the data and proceeds from there. Our contribution is to explain how subject covariates can be incorporated into a PDA analysis for graphical exploration of patterns in the data. |
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| Keywords: | CAEP curves Differential operator Low-dimensional approximation |
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