Methods for scalar-on-function regression
TL;DR: Some of the main approaches to how to fit regression models with scalar responses and functional data points as predictors are reviewed, categorizing the basic model types as linear, nonlinear and nonparametric.
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Abstract: Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.
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Recent advances in functional data analysis and high-dimensional statistics
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A general framework for functional regression modelling
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TL;DR: A comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data is discussed, allowing the adaptation of a large body of existing methods for these novel tasks.
Grouped functional time series forecasting: An application to age-specific mortality rates
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TL;DR: In this article, the authors proposed a bootstrap method for reconciling interval forecasts of age-specific mortality rates, where age is considered as a continuum and grouped functional time series methods were used to produce point forecasts of mortality rates that are aggregated appropriately across different disaggregation factors.
High-dimensional functional time series forecasting: An application to age-specific mortality rates
TL;DR: This paper addresses the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure through Dynamic functional principal component analysis and uses the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved.
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Time series extrinsic regression: Predicting numeric values from time series data.
TL;DR: In this paper, the authors study time series extrinsic regression (TSER), a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification.
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