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2013 Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
Hervé Cardot, Camelia Goga, Pauline Lardin
Electron. J. Statist. 7: 562-596 (2013). DOI: 10.1214/13-EJS779

Abstract

When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator are uniformly consistent. Then, under additional assumptions, we prove a functional central limit theorem and we assess rigorously a fast technique based on simulations of Gaussian processes which is employed to build asymptotic confidence bands. The accuracy of the variance function estimator is evaluated on a real dataset of sampled electricity consumption curves measured every half an hour over a period of one week.

Citation

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Hervé Cardot. Camelia Goga. Pauline Lardin. "Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data." Electron. J. Statist. 7 562 - 596, 2013. https://doi.org/10.1214/13-EJS779

Information

Published: 2013
First available in Project Euclid: 14 March 2013

zbMATH: 1336.62043
MathSciNet: MR3035266
Digital Object Identifier: 10.1214/13-EJS779

Subjects:
Primary: 62L20
Secondary: 60F05

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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