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- Articles and reports: 12-001-X202300200016Description: In this discussion, I will present some additional aspects of three major areas of survey theory developed or studied by Jean-Claude Deville: calibration, balanced sampling and the generalized weight-share method.Release date: 2024-01-03
- Articles and reports: 12-001-X202300100011Description: The definition of statistical units is a recurring issue in the domain of sample surveys. Indeed, not all the populations surveyed have a readily available sampling frame. For some populations, the sampled units are distinct from the observation units and producing estimates on the population of interest raises complex questions, which can be addressed by using the weight share method (Deville and Lavallée, 2006). However, the two populations considered in this approach are discrete. In some fields of study, the sampled population is continuous: this is for example the case of forest inventories for which, frequently, the trees surveyed are those located on plots of which the centers are points randomly drawn in a given area. The production of statistical estimates from the sample of trees surveyed poses methodological difficulties, as do the associated variance calculations. The purpose of this paper is to generalize the weight share method to the continuous (sampled population) ? discrete (surveyed population) case, from the extension proposed by Cordy (1993) of the Horvitz-Thompson estimator for drawing points carried out in a continuous universe.Release date: 2023-06-30
- Articles and reports: 12-001-X202100200005Description:
Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.
Release date: 2022-01-06 - Articles and reports: 12-001-X201800254952Description:
Panel surveys are frequently used to measure the evolution of parameters over time. Panel samples may suffer from different types of unit non-response, which is currently handled by estimating the response probabilities and by reweighting respondents. In this work, we consider estimation and variance estimation under unit non-response for panel surveys. Extending the work by Kim and Kim (2007) for several times, we consider a propensity score adjusted estimator accounting for initial non-response and attrition, and propose a suitable variance estimator. It is then extended to cover most estimators encountered in surveys, including calibrated estimators, complex parameters and longitudinal estimators. The properties of the proposed variance estimator and of a simplified variance estimator are estimated through a simulation study. An illustration of the proposed methods on data from the ELFE survey is also presented.
Release date: 2018-12-20 - 5. Linearization versus bootstrap for variance estimation of the change between Gini indexes ArchivedArticles and reports: 12-001-X201800154926Description:
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.
Release date: 2018-06-21 - Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - 8. Stratified balanced sampling ArchivedArticles and reports: 12-001-X200900110888Description:
In the selection of a sample, a current practice is to define a sampling design stratified on subpopulations. This reduces the variance of the Horvitz-Thompson estimator in comparison with direct sampling if the strata are highly homogeneous with respect to the variable of interest. If auxiliary variables are available for each individual, sampling can be improved through balanced sampling within each stratum, and the Horvitz-Thompson estimator will be more precise if the auxiliary variables are strongly correlated with the variable of interest. However, if the sample allocation is small in some strata, balanced sampling will be only very approximate. In this paper, we propose a method of selecting a sample that is balanced across the entire population while maintaining a fixed allocation within each stratum. We show that in the important special case of size-2 sampling in each stratum, the precision of the Horvitz-Thompson estimator is improved if the variable of interest is well explained by balancing variables over the entire population. An application to rotational sampling is also presented.
Release date: 2009-06-22
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Articles and reports (8)
Articles and reports (8) ((8 results))
- Articles and reports: 12-001-X202300200016Description: In this discussion, I will present some additional aspects of three major areas of survey theory developed or studied by Jean-Claude Deville: calibration, balanced sampling and the generalized weight-share method.Release date: 2024-01-03
- Articles and reports: 12-001-X202300100011Description: The definition of statistical units is a recurring issue in the domain of sample surveys. Indeed, not all the populations surveyed have a readily available sampling frame. For some populations, the sampled units are distinct from the observation units and producing estimates on the population of interest raises complex questions, which can be addressed by using the weight share method (Deville and Lavallée, 2006). However, the two populations considered in this approach are discrete. In some fields of study, the sampled population is continuous: this is for example the case of forest inventories for which, frequently, the trees surveyed are those located on plots of which the centers are points randomly drawn in a given area. The production of statistical estimates from the sample of trees surveyed poses methodological difficulties, as do the associated variance calculations. The purpose of this paper is to generalize the weight share method to the continuous (sampled population) ? discrete (surveyed population) case, from the extension proposed by Cordy (1993) of the Horvitz-Thompson estimator for drawing points carried out in a continuous universe.Release date: 2023-06-30
- Articles and reports: 12-001-X202100200005Description:
Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.
Release date: 2022-01-06 - Articles and reports: 12-001-X201800254952Description:
Panel surveys are frequently used to measure the evolution of parameters over time. Panel samples may suffer from different types of unit non-response, which is currently handled by estimating the response probabilities and by reweighting respondents. In this work, we consider estimation and variance estimation under unit non-response for panel surveys. Extending the work by Kim and Kim (2007) for several times, we consider a propensity score adjusted estimator accounting for initial non-response and attrition, and propose a suitable variance estimator. It is then extended to cover most estimators encountered in surveys, including calibrated estimators, complex parameters and longitudinal estimators. The properties of the proposed variance estimator and of a simplified variance estimator are estimated through a simulation study. An illustration of the proposed methods on data from the ELFE survey is also presented.
Release date: 2018-12-20 - 5. Linearization versus bootstrap for variance estimation of the change between Gini indexes ArchivedArticles and reports: 12-001-X201800154926Description:
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.
Release date: 2018-06-21 - Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - 8. Stratified balanced sampling ArchivedArticles and reports: 12-001-X200900110888Description:
In the selection of a sample, a current practice is to define a sampling design stratified on subpopulations. This reduces the variance of the Horvitz-Thompson estimator in comparison with direct sampling if the strata are highly homogeneous with respect to the variable of interest. If auxiliary variables are available for each individual, sampling can be improved through balanced sampling within each stratum, and the Horvitz-Thompson estimator will be more precise if the auxiliary variables are strongly correlated with the variable of interest. However, if the sample allocation is small in some strata, balanced sampling will be only very approximate. In this paper, we propose a method of selecting a sample that is balanced across the entire population while maintaining a fixed allocation within each stratum. We show that in the important special case of size-2 sampling in each stratum, the precision of the Horvitz-Thompson estimator is improved if the variable of interest is well explained by balancing variables over the entire population. An application to rotational sampling is also presented.
Release date: 2009-06-22
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