Consistency of the mean and the principal components of spatially distributed functional data

DOI10.3150/12-BEJ418zbMath1457.62193arXiv1104.3074MaRDI QIDQ2435212

Siegfried Hörmann, Piotr S. Kokoszka

Publication date: 4 February 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3074

zbMATH Keywords

estimationconsistencyspatial dependencefunctional dataspatial sampling designfunctional principal components

Mathematics Subject Classification ID

Inference from spatial processes (62M30) Random fields; image analysis (62M40) Factor analysis and principal components; correspondence analysis (62H25) Functional data analysis (62R10)

Related Items

Test of Weak Separability for Spatially Stationary Functional Field ⋮ On estimation and prediction in spatial functional linear regression model ⋮ Functional data analysis with rough sample paths? ⋮ Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends ⋮ Dependent functional data ⋮ An introduction to functional data analysis and a principal component approach for testing the equality of mean curves ⋮ P. Secchi, S. Vantini and V. Vitelli: ``Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan ⋮ Discussion of ``Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan by P. Secchi, S. Vantini, and V. Vitelli ⋮ Discussion of ``Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan by Piercesare Secchi, Simone Vantini and Valeria Vitelli ⋮ Empirical properties of forecasts with the functional autoregressive model

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Portmanteau Test of Independence for Functional Observations
• Central limit theorems and uniform laws of large numbers for arrays of random fields
• Resampling methods for spatial regression models under a class of stochastic designs
• The oscillation behavior of empirical processes: The multivariate case
• Weakly dependent functional data
• Common functional principal components
• Consistency of restricted maximum likelihood estimators of principal components
• Practically applicable central limit theorem for spatial statistics
• Fixed-domain asymptotic properties of tapered maximum likelihood estimators
• The order of magnitude of the moments of the modulus of continuity of multiparameter Poisson and empirical processes
• On the central limit theorem for stationary mixing random fields
• Classes of linear operators. Vol. I
• Covariance inequalities for strongly mixing processes
• Linear processes in function spaces. Theory and applications
• Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields
• Covariate adjusted functional principal components analysis for longitudinal data
• Functional data analysis.
• Functional Data Analysis with R and MATLAB
• Functional Principal Component Regression and Functional Partial Least Squares
• Tests for Error Correlation in the Functional Linear Model
• On Properties of Functional Principal Components Analysis
• Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics
• 8. Functional Data Analysis