Assessing extrema of empirical principal component functions

DOI10.1214/009053606000000371zbMath1113.62074arXivmath/0608025OpenAlexW4298166670MaRDI QIDQ2500461

Céline Vial, Hall, Peter

Publication date: 24 August 2006

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

Full work available at URL: https://arxiv.org/abs/math/0608025

zbMATH Keywords

bootstrapperturbationturning pointfunctional data analysismodeprincipal components analysissubsamplebootstrap likelihoodKarhunen-Loeve representationshoulder point

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Statistics of extreme values; tail inference (62G32) Nonparametric statistical resampling methods (62G09)

Related Items

Minimax adaptive tests for the functional linear model

Uses Software

• fda (R)
• SiZer

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
• Gait analysis and the bootstrap
• Curves discrimination: a nonparametric functional approach
• Perturbation of spectral subspaces and solution of linear operator equations
• The dip test of unimodality
• Principal components analysis of sampled functions
• Some asymptotics for multimodality tests based on kernel density estimates
• Subsampling
• Nonparametric testing of the existence of modes
• On the asymptotic normality of kernel regression estimators of the mode in the nonparametric random design model.
• Kernel-based functional principal components
• Linear processes in function spaces. Theory and applications
• Applied functional data analysis. Methods and case studies
• Weak convergence for the covariance operators of a Hilbertian linear process.
• Functional canonical analysis for square integrable stochastic processes
• Scale space view of curve estimation.
• Least squares estimators of the mode of a unimodal regression function
• Density estimation under qualitative assumptions in higher dimensions
• Smoothed functional principal components analysis by choice of norm
• Functional data analysis.
• Mode testing via the excess mass estimate
• Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves
• Excess Mass Estimates and Tests for Multimodality
• Functional Classification in Hilbert Spaces
• Calibrating the Excess Mass and Dip Tests of Modality
• A Graphical Technique for Determining the Number of Components in a Mixture of Normals
• Regression Analysis for a Functional Response
• Nonparametric estimation of smoothed principal components analysis of sampled noisy functions
• Principal component models for sparse functional data
• Test of Significance When Data Are Curves
• SiZer for Exploration of Structures in Curves
• Varying-coefficient models and basis function approximations for the analysis of repeated measurements
• On nonparametric kernel estimation of the mode of the regression function in the random design model
• Nonparametric models for functional data, with application in regression, time series prediction and curve discrimination
• Étude asymptotique d'un estimateur spline hybride pour le modèle linéaire fonctionnel
• Statistical analysis of temporal evolution in single-neuron firing rates
• A nonlinear PCA based on manifold approximation