Prediction in functional linear regression

By Tommaso Cai, Peter Hall. 2006

619 citations recorded by the source corpus.

Supported in part by NSF Grant DMS-03-06576 and a grant from the Australian Research Council.

View Paper: https://www.semanticscholar.org/paper/956ffdff7a6d9a662a40f2ca85fada96b7e255dd

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In Statistics and Probability

Citations in the corpus

Shrinkage estimation and selection for multiple functional regression (2011, methodology): “Some recent developments in functional regression include Yao, Müller, and Wang (2005); Cai and Hall (2006); Crambes, Kneip, and Sarda (2009); Yuan and Cai (2010). The literature contains an impressive range of functional analysis tools for various problems. The traditional approach, carefully docum”
Presmoothing in Functional Linear Regression (2012, methodology): “Second methodology is based on functional principal components analysis (FPCA), as developed and analyzed by Cardot, Ferraty, and Sarda (1999) Cardot, Ferraty, and Sarda (2003), Cai and Hall (2006), Hall and Hosseini-Nasab (2006), Hall and Horowitz (2007), and Cardot, Mas, and Sarda (2007). The FPCA”
Adaptive Global Testing for Functional Linear Models (2014, methodology): “The problem of prediction was studied by Cai and Hall (2006).”
Factor models and variable selection in high-dimensional regression analysis (2011, background): “…functional linear regression are, for example, presented in Ramsay and Dalzell (1991), Cardot, Ferraty and Sarda (1999), Cuevas, Febrero and Fraiman (2002), Yao, Müller and Wang (2005), Cai and Hall (2006), Hall and Horowitz (2007), Cardot, Mas and Sarda (2007) and Crambes, Kneip and Sarda (2009).”
Functional Additive Models (2008, methodology): “Recent asymptotic studies of estimation in functional linear regression models with scalar response and fully observed predictor trajectories include those of Cai and Hall (2006) and Hall and Horowitz (2007).”
Functional time series approach for forecasting very short-term electricity demand (2013, background): “[10], Cai and Hall [5], Hall et al.”
Continuously additive models for nonlinear functional regression (2013, background): “…at U niversity of T oronto L ibrary on O ctober 2, 2013 http://biom et.oxfordjournals.org/ D ow nloaded from at U niversity of T oronto L ibrary on O ctober 2, 2013 http://biom et.oxfordjournals.org/ D ow nloaded from see, e.g., Cai & Hall (2006), Cardot et al. (2007) and Crambes et al. (2009).”
Nonlinear estimation for linear inverse problems with error in the operator (2008, background): “Hall and Horowitz [13] obtain in their Theorem 4.2 the linear rate of Section 3 when replacing their terms as follows: ε= δ = n−1/2, t= α, s= β + 1/2, d= 1.”
Functional Data Analysis (2016, background): “An interesting phenomenon is that prediction for model (9) follows a diﬀerent paradigm in which √ n convergence is attainable if the predictor X is suﬃciently smooth and the eigenvalues of predictor processes are well behaved (Cai & Hall 2006).”
Functional data: local linear estimation of the conditional density and its application (2013, background): “In 21 , the same idea is expressed stating that optimizing in b is an infinite-dimensional problem.”
Locally Sparse Estimator for Functional Linear Regression Models (2017, methodology): “Alternative smooth estimators that are based on spectral decomposition of the covariance function of X (t ) were developed by Cardot, Ferraty, and Sarda (2003), Cai and Hall (2006), and Hall and Horowitz (2007).”
Minimax adaptive tests for the Functional Linear model (2012, background): “The theoretical properties of these classes of estimators have been investigated from different viewpoints: prediction [6, 9, 13, 36] (estimation of 〈Xn+1, θ〉 where Xn+1 follows the same distribution as X), pointwise prediction [4] (estimation of 〈x, θ〉 for a fixed x ∈ H) or the inverse problem [11,”
Truncated linear models for functional data (2014, methodology): “…and Wu et al. (2010), among others, developed methodology for functional linear regression in the context of longitudinal data analysis; Cai and Hall (2006) and Apanasovich and Goldstein (2008) addressed mean-squared prediction error in functional linear regression; and Cardot et al. (2007),…”
A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data (2007, methodology): “The eigenfunctions give a nice basis for representing functional data, and hence are very useful in problems related to model building and prediction (see, e.g., Cardot, Ferraty, and Sarda 1999; Cai and Hall 2006; Hall and Horowitz 2007).”
Regression imputation in the functional linear model with missing values in the response (2019, background): “Among this, the functional linear model has received a special attention (see [24, 4, 5, 3, 15, 10, 6, 30] for main references).”
Partially functional linear regression in high dimensions (2016, methodology): “One common approach is functional principal component analysis, which has been studied by Rice & Silverman (1991), Yao et al. (2005b), Cai & Hall (2006), Hall et al. (2006), Hall & Horowitz (2007) and Zhang & Chen (2007), among others.”