Deciding the dimension of effective dimension reduction space for functional and high-dimension\-al data

DOI10.1214/10-AOS816zbMath1200.62115arXiv1011.2620OpenAlexW1998660026MaRDI QIDQ605938

Tailen Hsing, Yehua Li

Publication date: 15 November 2010

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

Full work available at URL: https://arxiv.org/abs/1011.2620

zbMATH Keywords

dimension reductionelliptically contoured distributionprincipal componentsfunctional data analysisadaptive Neyman test

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Factor analysis and principal components; correspondence analysis (62H25) Asymptotic properties of nonparametric inference (62G20) Linear regression; mixed models (62J05) Sequential statistical analysis (62L10) Applications of functional analysis in probability theory and statistics (46N30)

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Uses Software

• fda (R)
• gss
• RSIR

Cites Work

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• Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
• Prediction in functional linear regression
• Dimension reduction in functional regression with applications
• Smoothing splines estimators for functional linear regression
• An RKHS formulation of the inverse regression dimension-reduction problem
• An integral transform method for estimating the central mean and central subspaces
• On the theory of elliptically contoured distributions
• The asymptotic distribution of singular values with applications to canonical correlations and correspondence analysis
• Generalized functional linear models
• Asymptotic distribution of coordinates on high dimensional spheres
• Functional data analysis.
• Estimation in generalized linear models for functional data via penalized likelihood
• Properties of principal component methods for functional and longitudinal data analysis
• Statistical inferences for functional data
• Metric spaces and completely monontone functions
• Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression
• Sliced Inverse Regression for Dimension Reduction
• Measurement Error Regression with Unknown Link: Dimension Reduction and Data Visualization
• Determining the Dimensionality in Sliced Inverse Regression
• Functional sliced inverse regression analysis
• Test of Significance When Data Are Curves
• An Adaptive Estimation of Dimension Reduction Space
• On Properties of Functional Principal Components Analysis
• Functional Adaptive Model Estimation
• Smoothing spline ANOVA models