An RKHS formulation of the inverse regression dimension-reduction problem

DOI10.1214/07-AOS589zbMath1162.62053arXiv0904.0076MaRDI QIDQ1020976

Tailen Hsing, Haobo Ren

Publication date: 4 June 2009

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.0076

zbMATH Keywords

functional data analysissliced inverse regression

Mathematics Subject Classification ID

Multivariate analysis (62H99) Estimation in multivariate analysis (62H12) Linear inference, regression (62J99) Inference from stochastic processes (62M99) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (22)

Dimension reduction for functional data based on weak conditional moments ⋮ Functional \(k\)-means inverse regression ⋮ A Review on Sliced Inverse Regression, Sufficient Dimension Reduction, and Applications ⋮ Functional sufficient dimension reduction through average Fréchet derivatives ⋮ Stochastic functional linear models and Malliavin calculus ⋮ Partially function linear error-in-response models with validation data ⋮ Deciding the dimension of effective dimension reduction space for functional and high-dimension\-al data ⋮ Predictive power of principal components for single-index model and sufficient dimension reduction ⋮ Functional sufficient dimension reduction: convergence rates and multiple functional case ⋮ Multiresolution Hilbert approach to multidimensional Gauss-Markov processes ⋮ Estimation of inverse mean: an orthogonal series approach ⋮ On functional logistic regression: some conceptual issues ⋮ A general theory for nonlinear sufficient dimension reduction: formulation and estimation ⋮ Principal support vector machines for linear and nonlinear sufficient dimension reduction ⋮ Double-slicing assisted sufficient dimension reduction for high-dimensional censored data ⋮ An RKHS model for variable selection in functional linear regression ⋮ Optimal rate for prediction when predictor and response are functions ⋮ Inverse regression for longitudinal data ⋮ On the predictive potential of kernel principal components ⋮ Functional linear regression with points of impact ⋮ Gradient-Based Kernel Dimension Reduction for Regression ⋮ Dimension reduction for functional regression with a binary response

Uses Software

• fda (R)
• gss

Cites Work

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