Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data

DOI10.1214/13-EJS779zbMath1336.62043arXiv1204.6382MaRDI QIDQ1951128

Hervé Cardot, Camelia Goga, Pauline Lardin

Publication date: 29 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.6382

zbMATH Keywords

covariance functioncalibrationlinear interpolationsurvey samplingHorvitz-Thompson estimatorfunctional linear modelGREGHájek estimator

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Sampling theory, sample surveys (62D05) Nonparametric tolerance and confidence regions (62G15)

Related Items

Functional principal subspace sampling for large scale functional data analysis, Depth-based nonparametric description of functional data, with emphasis on use of spatial depth, Model-Assisted Estimators with Auxiliary Functional Data, Model-Assisted Estimation Through Random Forests in Finite Population Sampling, On estimators of the mean of Infinite dimensional data in finite populations, Exact balanced random imputation for sample survey data, Preserving the distribution function in surveys in case of imputation for zero inflated data, Asymptotic efficiency of the calibration estimator in a high-dimensional data setting, Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the use of the bootstrap for estimating functions with functional data
• Properties of design-based functional principal components analysis
• Model assisted survey sampling
• Conditions for sample-continuity and the central limit theorem
• Local sample path properties of Gaussian fields
• Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes
• Local polynomial regresssion estimators in survey sampling.
• Weak convergence and empirical processes. With applications to statistics
• Approximation of rejective sampling inclusion probabilities and application to high order correlations
• Kernel regression with functional response
• Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
• Functional data analysis.
• Simultaneous confidence bands for nonparametric regression with functional data
• Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
• Sampling Statistics
• Calibration Estimators in Survey Sampling
• Asymptotic Statistics
• Regression Analysis for a Functional Response
• Survey Design Under the Regression Superpopulation Model
• Rotation sampling for functional data
• Random Fields and Geometry
• Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling Designs
• Conditional Functional Principal Components Analysis