The historical functional linear model

By N. Malfait, James O. Ramsay. 2003

154 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e6aea0a4b6ff94d9b7f6ca703bb78c588d2e7d58

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In Signal Processing

Citations in the corpus

Functional Regression (2014, unknown): “Malfait & Ramsay (2003) representedB(s, t) using custom basis functions φ(s, t) that are tent-like piecewise linear functions on some grid, constructed to ensure the s ≤ t constraint, and fit a model with iid errors.”
Twenty years of P-splines (2015, background): “When each element of y is not a scalar but a time series, as is x, the historical functional linear model (HFLM) assumes that in principle all previous x can influence the elements of y (Malfait and Ramsay, 2003).”
The functional linear array model (2015, background): “For instance, if functional response and covariate are observed over time, the historical functional linear model (Malfait and Ramsay, 2003; Harezlak et al., 2007) (Y(t)|X = x) = ∫ t t−ı x(s)ˇ(s, t)ds can be of interest, where only lagged past values of the functional covariate are used to model the”
Asymptotics of prediction in functional linear regression with functional outputs (2009, methodology): “A major reference in this domain is the monograph by Ramsay and Silverman [19] which gives an overview about the philosophy and the basic models involving functional data.”
A general framework for functional regression modelling (2017, background): “In cases where functional responses and functional covariates are observed over the same time interval, it is often more meaningful to relate the response only to values of the covariate in the past (so-called historical models, Malfait and Ramsay, 2003).”
Functional data analysis for volatility (2011, methodology): “Applications of FDA to economic data have been considered before, e.g., by Malfait and Ramsay (2003) and Ramsay and Ramsey (2001), but there do not seem to exist any specific FDA approaches for finance to date.”
Peter Hall, functional data analysis and random objects (2016, background): “This problem is related to the historical functional linear model (Malfait and Ramsay, 2003) and extends history versions of functional varying coefficient models (Sentürk and Müller, 2010).”
Tests for Error Correlation in the Functional Linear Model (2010, methodology): “…out as a particularly useful tool, and has consequently been thoroughly studied and extensively applied; see Cuevas, Febrero, and Fraiman (2002), Malfait and Ramsay (2003), Cardot et al. (2003), Chiou, Müller, and Wang (2004), Müller and Stadtmüller (2005), Yao, Müller, and Wang (2005a, 2005b),…”
Functional Data Analysis (2016, methodology): “This has been referred to as the “historical functional linear model” (Malfait & Ramsay 2003), because only the history of the covariate is used to model the response process.”
Functional Additive Models (2008, background): “…regression for longitudinal, (i.e., sparse), irregular, and noisy data (Yao, Müller, and Wang 2005b); varying-coefficient functional models (Malfait and Ramsay 2003; Fan and Zhang 2000; Fan, Yao, and Cai 2003); wavelet-based functional models (Morris, Vannucci, Brown, and Carroll 2003);…”