0000000000627329
AUTHOR
Etienne Josserand
showing 5 related works from this author
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
2013
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of …
Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
2009
When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose here a Horvitz--Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove under mild regularity conditions that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional assumptions on the sampling design we state a functional Central Limit Theorem and deduce asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal …
Semiparametric Models with Functional Responses in a Model Assisted Survey Sampling Setting : Model Assisted Estimation of Electricity Consumption Cu…
2010
This work adopts a survey sampling point of view to estimate the mean curve of large databases of functional data. When storage capacities are limited, selecting, with survey techniques a small fraction of the observations is an interesting alternative to signal compression techniques. We propose here to take account of real or multivariate auxiliary information available at a low cost for the whole population, with semiparametric model assisted approaches, in order to improve the accuracy of Horvitz-Thompson estimators of the mean curve. We first estimate the functional principal components with a design based point of view in order to reduce the dimension of the signals and then propose s…
Survey sampling for functionnal data : building asymptotic confidence bands and considering auxiliary information
2011
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function, without being obligated to store all the data. In this thesis, we propose a Horvitz–Thompson estimator of the mean trajectory, and with additional assumptions on the sampling design, we state a functional Central Limit Theorem and deduce asymptotic confidence bands. For a fixed sample size, we show that stratified sampling can greatly improve the estimation compared to simple random sampling. In addition, we extend Neyman’s rule of optimal allocation to the functional context. Taking into accoun…
Semiparametric models with functional responses in a survey sampling setting : model assisted estimation of electricity consumption curve
2010
International audience; Ce travail adopte une approche de type sondage quand le but est d'estimer une courbe moyenne d'une grande base de données de données fonctionnelles. Lorsque les capacités de stockage sont limitées, grâce aux techniques de sondage, une petite partie des observations est une alternative intéressante par rapport aux techniques de compression. Nous proposons ici de prendre en considération une information auxiliaire réelle ou multivariée obtenu à moindre coût sur la population toute entière, avec une approche semiparamétrique de type modèle assisté, dans le but d'améliorer les estimateurs d'Horvitz-Thompson de la courbe moyenne. D'abord, nous estimerons les composantes p…