Analysis

Description: In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.

Description: Jean-Claude Deville is one of the most prominent researcher in survey sampling theory and practice. His research on balanced sampling, indirect sampling and calibration in particular is internationally recognized and widely used in official statistics. He was also a pioneer in the field of functional data analysis. This discussion gives us the opportunity to recognize the immense work he has accomplished, and to pay tribute to him. In the first part of this article, we recall briefly his contribution to the functional principal analysis. We also detail some recent extension of his work at the intersection of the fields of functional data analysis and survey sampling. In the second part of this paper, we present some extension of Jean-Claude’s work in indirect sampling. These extensions are motivated by concrete applications and illustrate Jean-Claude’s influence on our work as researchers.

Description:

Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory.

In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.

Description:

This paper investigates the linearization and bootstrap variance estimation for the Gini coefficient and the change between Gini indexes at two periods of time. For the one-sample case, we use the influence function linearization approach suggested by Deville (1999), the without-replacement bootstrap suggested by Gross (1980) for simple random sampling without replacement and the with-replacement of primary sampling units described in Rao and Wu (1988) for multistage sampling. To obtain a two-sample variance estimator, we use the linearization technique by means of partial influence functions (Goga, Deville and Ruiz-Gazen, 2009). We also develop an extension of the studied bootstrap procedures for two-dimensional sampling. The two approaches are compared on simulated data.

Description:

When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.

Description: In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.

Description: Jean-Claude Deville is one of the most prominent researcher in survey sampling theory and practice. His research on balanced sampling, indirect sampling and calibration in particular is internationally recognized and widely used in official statistics. He was also a pioneer in the field of functional data analysis. This discussion gives us the opportunity to recognize the immense work he has accomplished, and to pay tribute to him. In the first part of this article, we recall briefly his contribution to the functional principal analysis. We also detail some recent extension of his work at the intersection of the fields of functional data analysis and survey sampling. In the second part of this paper, we present some extension of Jean-Claude’s work in indirect sampling. These extensions are motivated by concrete applications and illustrate Jean-Claude’s influence on our work as researchers.

Description:

Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory.

In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.

Description:

This paper investigates the linearization and bootstrap variance estimation for the Gini coefficient and the change between Gini indexes at two periods of time. For the one-sample case, we use the influence function linearization approach suggested by Deville (1999), the without-replacement bootstrap suggested by Gross (1980) for simple random sampling without replacement and the with-replacement of primary sampling units described in Rao and Wu (1988) for multistage sampling. To obtain a two-sample variance estimator, we use the linearization technique by means of partial influence functions (Goga, Deville and Ruiz-Gazen, 2009). We also develop an extension of the studied bootstrap procedures for two-dimensional sampling. The two approaches are compared on simulated data.

Description:

When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.