The Experts below are selected from a list of 1413 Experts worldwide ranked by ideXlab platform
Hervé Cardot - One of the best experts on this subject based on the ideXlab platform.
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variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
Scandinavian Journal of Statistics, 2014Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes whose variance function is given by the Hajek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.
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Variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
2013Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that we can get a uniformly convergent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for the rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes with variance function given by the Hájek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.
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horvitz Thompson Estimators for functional data asymptotic confidence bands and optimal allocation for stratified sampling
Biometrika, 2011Co-Authors: Hervé Cardot, Etienne JosserandAbstract: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 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 obtain asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal allocation rule, considering a mean variance criterion. These techniques are illustrated by a test population of Ne18 902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week. We show that stratification can substantially improve both the accuracy of the Estimators and reduce the width of the global confidence bands compared with simple random sampling without replacement. Copyright 2011, Oxford University Press.
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horvitz Thompson Estimators for functional data asymptotic confidence bands and optimal allocation for stratified sampling
arXiv: Methodology, 2009Co-Authors: Hervé Cardot, Etienne JosserandAbstract: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 allocation rule considering a mean variance criterion. These techniques are illustrated by means of a test population of N=18902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week. We show that stratification can substantially improve both the accuracy of the Estimators and reduce the width of the global confidence bands compared to simple random sampling without replacement.
Pauline Lardin - One of the best experts on this subject based on the ideXlab platform.
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variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
Scandinavian Journal of Statistics, 2014Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes whose variance function is given by the Hajek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.
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Variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
2013Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that we can get a uniformly convergent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for the rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes with variance function given by the Hájek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.
Anne Ruiz-gazen - One of the best experts on this subject based on the ideXlab platform.
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Estimation Under Cross-Classified Sampling With Application to a Childhood Survey
Journal of the American Statistical Association, 2017Co-Authors: Hélène Juillard, Guillaume Chauvet, Anne Ruiz-gazenAbstract:The cross-classified sampling design consists in drawing samples from a two-dimensional population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies in the French Longitudinal Survey on Childhood, by crossing a sample of maternity units and a sample of days. We propose to derive a general theory of estimation for this sampling design. We consider the Horvitz–Thompson Estimator for a total, and show that the cross-classified design will usually result in a loss of efficiency as compared to the widespread two-stage design. We obtain the asymptotic distribution of the Horvitz–Thompson Estimator and several unbiased variance Estimators. Facing the problem of possibly negative values, we propose simplified nonnegative variance Estimators and study their bias under a super-population model. The proposed Estimators are compared for totals and ratios on simulated data. An application on real data from the French Longitudinal Survey on Childhood is also presented, and we make some recommendations. Supplementary materials for this article are available online.
Guillaume Chauvet - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic properties of pivotal sampling with application to spatial sampling
2019Co-Authors: Guillaume Chauvet, Ronan Le GleutAbstract:Unequal probability sampling without replacement is commonly used for sample selection. To produce Estimators with associated condence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz-Thompson Estimator are desirable. These properties have been mainly studied for large entropy sampling designs. On the other hand, spatial sampling designs rather make use of sampling algorithms which take into account the order of units in the population, like systematic sampling or pivotal sampling. So far, the statistical properties of such procedures have not been investigated. In this work, we study the asymptotic properties of the pivotal sampling design. Under mild assumptions, we prove that the Horvitz-Thompson Estimator is asymptotically normally distributed and that a conservative variance Estimator can always be computed. We also introduce a general spatial sampling design which is spatially balanced, which possesses good statistical properties and which is computationally very ecient, even for large databases.
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Inference for two-stage sampling designs with application to a panel for urban policy
2018Co-Authors: Guillaume Chauvet, Audrey-anne ValléeAbstract:Two-stage sampling designs are commonly used for household and health surveys. To produce reliable Estimators with assorted confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz-Thompson Estimator are desirable, along with the consistency of assorted variance Estimators. These properties have been mainly studied for single-stage sampling designs. In this work, we prove the consistency of the Horvitz-Thompson Estimator and of associated variance Estimators for a general class of two-stage sampling designs, under mild assumptions. We also study two-stage sampling with a large entropy sampling design at the first stage, and prove that the Horvitz-Thompson Estimator is asymptotically normally distributed through a coupling argument. When the first-stage sampling fraction is negligible, simplified variance Estimators which do not require estimating the variance within the Primary Sampling Units are proposed, and shown to be consistent. An application to a panel for urban policy, which is the initial motivation for this work, is also presented.
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Estimation Under Cross-Classified Sampling With Application to a Childhood Survey
Journal of the American Statistical Association, 2017Co-Authors: Hélène Juillard, Guillaume Chauvet, Anne Ruiz-gazenAbstract:The cross-classified sampling design consists in drawing samples from a two-dimensional population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies in the French Longitudinal Survey on Childhood, by crossing a sample of maternity units and a sample of days. We propose to derive a general theory of estimation for this sampling design. We consider the Horvitz–Thompson Estimator for a total, and show that the cross-classified design will usually result in a loss of efficiency as compared to the widespread two-stage design. We obtain the asymptotic distribution of the Horvitz–Thompson Estimator and several unbiased variance Estimators. Facing the problem of possibly negative values, we propose simplified nonnegative variance Estimators and study their bias under a super-population model. The proposed Estimators are compared for totals and ratios on simulated data. An application on real data from the French Longitudinal Survey on Childhood is also presented, and we make some recommendations. Supplementary materials for this article are available online.
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a note on the consistency of the narain horvitz Thompson Estimator
arXiv: Methodology, 2014Co-Authors: Guillaume ChauvetAbstract:For the Narain-Horvitz-Thompson Estimator to have usual asymptotic properties such as consistency, some conditions on the sampling design and on the variable of interest are needed. Cardot et al. (2010) give some sufficient conditions for the mean square consistency, but one of them is usually difficult to prove or does not hold for some unequal probability sampling designs. We propose alternative conditions for the mean square consistency of the Narain-Horvitz-Thompson Estimator. A specific result is also proved in case when a martingale sampling algorithm is used, which implies consistency under a fast algorithm for the cube method.
Camelia Goga - One of the best experts on this subject based on the ideXlab platform.
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variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
Scandinavian Journal of Statistics, 2014Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes whose variance function is given by the Hajek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.
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Variance estimation and asymptotic confidence bands for the mean Estimator of sampled functional data with high entropy unequal probability sampling designs
2013Co-Authors: Hervé Cardot, Camelia Goga, Pauline LardinAbstract:For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson Estimator can be approximated by the Hájek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that we can get a uniformly convergent Estimator of the variance function of the Horvitz-Thompson Estimator of the mean function. Rates of convergence to the true variance function are given for the rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes with variance function given by the Hájek formula. Finally, the accuracy of the proposed variance Estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.