Regression models using shapes of functions as predictors
Kyungmin Ahn,
J. Derek Tucker,
Wei Wu and
Anuj Srivastava
Computational Statistics & Data Analysis, 2020, vol. 151, issue C
Abstract:
Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the L2 inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. Here we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.
Keywords: Functional data analysis; Scalar-on-function regression; Functional single-index model; Function alignment; SRVF (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:151:y:2020:i:c:s0167947320301080
DOI: 10.1016/j.csda.2020.107017
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