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- Articles and reports: 12-001-X202100100007Description:
We consider the estimation of a small area mean under the basic unit-level model. The sum of the resulting model-dependent estimators may not add up to estimates obtained with a direct survey estimator that is deemed to be accurate for the union of these small areas. Benchmarking forces the model-based estimators to agree with the direct estimator at the aggregated area level. The generalized regression estimator is the direct estimator that we benchmark to. In this paper we compare small area benchmarked estimators based on four procedures. The first procedure produces benchmarked estimators by ratio adjustment. The second procedure is based on the empirical best linear unbiased estimator obtained under the unit-level model augmented with a suitable variable that ensures benchmarking. The third procedure uses pseudo-empirical estimators constructed with suitably chosen sampling weights so that, when aggregated, they agree with the reliable direct estimator for the larger area. The fourth procedure produces benchmarked estimators that are the result of a minimization problem subject to the constraint given by the benchmark condition. These benchmark procedures are applied to the small area estimators when the sampling rates are non-negligible. The resulting benchmarked estimators are compared in terms of relative bias and mean squared error using both a design-based simulation study as well as an example with real survey data.
Release date: 2021-06-24 - Articles and reports: 12-001-X202000100002Description:
Model-based methods are required to estimate small area parameters of interest, such as totals and means, when traditional direct estimation methods cannot provide adequate precision. Unit level and area level models are the most commonly used ones in practice. In the case of the unit level model, efficient model-based estimators can be obtained if the sample design is such that the sample and population models coincide: that is, the sampling design is non-informative for the model. If on the other hand, the sampling design is informative for the model, the selection probabilities will be related to the variable of interest, even after conditioning on the available auxiliary data. This will imply that the population model no longer holds for the sample. Pfeffermann and Sverchkov (2007) used the relationships between the population and sample distribution of the study variable to obtain approximately unbiased semi-parametric predictors of the area means under informative sampling schemes. Their procedure is valid for both sampled and non-sampled areas.
Release date: 2020-06-30 - Articles and reports: 12-001-X201900100009Description:
The demand for small area estimates by users of Statistics Canada’s data has been steadily increasing over recent years. In this paper, we provide a summary of procedures that have been incorporated into a SAS based production system for producing official small area estimates at Statistics Canada. This system includes: procedures based on unit or area level models; the incorporation of the sampling design; the ability to smooth the design variance for each small area if an area level model is used; the ability to ensure that the small area estimates add up to reliable higher level estimates; and the development of diagnostic tools to test the adequacy of the model. The production system has been used to produce small area estimates on an experimental basis for several surveys at Statistics Canada that include: the estimation of health characteristics, the estimation of under-coverage in the census, the estimation of manufacturing sales and the estimation of unemployment rates and employment counts for the Labour Force Survey. Some of the diagnostics implemented in the system are illustrated using Labour Force Survey data along with administrative auxiliary data.
Release date: 2019-05-07 - Articles and reports: 11-522-X20050019444Description:
There are several ways to improve data quality. One of them is to re-design and test questionnaires for ongoing surveys. The benefits of questionnaire re-design and testing include improving the accuracy by ensuring the questions collect the required data, as well as decreased response burden.
Release date: 2007-03-02 - 5. Variance estimation in two-phase sampling ArchivedArticles and reports: 11-522-X20030017600Description:
This paper extends the Sen-Yates-Grundy (SYG) variance estimators two-phase sampling designs with stratification at the second phase or both phases. It also develops SYG-type variance estimators of the two-phase regression estimators that make use of the first phase auxiliary data.
Release date: 2005-01-26 - 6. Closing remarks of the Symposium 2002: Modelling Survey Data for Social and Economic Research ArchivedArticles and reports: 11-522-X20020016751Description:
Closing remarks
Release date: 2004-09-13 - 7. Domain estimation using linear regression ArchivedArticles and reports: 12-001-X20040016995Description:
One of the main objectives of a sample survey is the computation of estimates of means and totals for specific domains of interest. Domains are determined either before the survey is carried out (primary domains) or after it has been carried out (secondary domains). The reliability of the associated estimates depends on the variability of the sample size as well as on the y-variables of interest. This variability cannot be controlled in the absence of auxiliary information for subgroups of the population. However, if auxiliary information is available, the estimated reliability of the resulting estimates can be controlled to some extent. In this paper, we study the potential improvements in terms of the reliability of domain estimates that use auxiliary information. The properties (bias, coverage, efficiency) of various estimators that use auxiliary information are compared using a conditional approach.
Release date: 2004-07-14 - 8. Double sampling ArchivedArticles and reports: 12-001-X20010026091Description:
The theory of double sampling is usually presented under the assumption that one of the samples is nested within the other. This type of sampling is called two-phase sampling. The first-phase sample provides auxiliary information (x) that is relatively inexpensive to obtain, whereas the second-phase sample: (b) to improve the estimate using a difference, ratio or regression estimator; or (c) to draw a sub-sample of non-respondent units. However, it is not necessary for one of the samples to be nested in the other or selected from the same frame. The case of non-nested double sampling is dealt with in passing in the classical works on sampling (Des Raj 1968, Cochrane 1977). This method is now used in several national statistical agencies. This paper consolidates double sampling by presenting it in a unified manner. Several examples of surveys used at Statistics Canada illustrate this unification.
Release date: 2002-02-28 - Articles and reports: 12-001-X19980013905Description:
Two-phase sampling designs offer a variety of possibilities for use of auxiliary information. We begin by reviewing the different forms that auxiliary information may take in two-phase surveys. We then set up the procedure by which this information is transformed into calibrated weights, which we use to construct efficient estimators of a population total. The calibration is done in two steps: (i) at the population level; (ii) at the level of the first-phase sample. We go on to show that the resulting calibration estimators are also derivable via regression fitting in two steps. We examine these estimators for a special case of interest, namely, when auxiliary information is available for population subgroups called calibration groups. Postrata are the simplest example of such groups. Estimation for domains of interest and variance estimation are also discussed. These results are illustrated by applying them to two-phase designs at Statistics Canada. The general theory for using auxiliary information in two-phase sampling is being incorporated into Statistics Canada's Generalized Estimation System.
Release date: 1998-07-31 - 10. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30
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Articles and reports (10)
Articles and reports (10) ((10 results))
- Articles and reports: 12-001-X202100100007Description:
We consider the estimation of a small area mean under the basic unit-level model. The sum of the resulting model-dependent estimators may not add up to estimates obtained with a direct survey estimator that is deemed to be accurate for the union of these small areas. Benchmarking forces the model-based estimators to agree with the direct estimator at the aggregated area level. The generalized regression estimator is the direct estimator that we benchmark to. In this paper we compare small area benchmarked estimators based on four procedures. The first procedure produces benchmarked estimators by ratio adjustment. The second procedure is based on the empirical best linear unbiased estimator obtained under the unit-level model augmented with a suitable variable that ensures benchmarking. The third procedure uses pseudo-empirical estimators constructed with suitably chosen sampling weights so that, when aggregated, they agree with the reliable direct estimator for the larger area. The fourth procedure produces benchmarked estimators that are the result of a minimization problem subject to the constraint given by the benchmark condition. These benchmark procedures are applied to the small area estimators when the sampling rates are non-negligible. The resulting benchmarked estimators are compared in terms of relative bias and mean squared error using both a design-based simulation study as well as an example with real survey data.
Release date: 2021-06-24 - Articles and reports: 12-001-X202000100002Description:
Model-based methods are required to estimate small area parameters of interest, such as totals and means, when traditional direct estimation methods cannot provide adequate precision. Unit level and area level models are the most commonly used ones in practice. In the case of the unit level model, efficient model-based estimators can be obtained if the sample design is such that the sample and population models coincide: that is, the sampling design is non-informative for the model. If on the other hand, the sampling design is informative for the model, the selection probabilities will be related to the variable of interest, even after conditioning on the available auxiliary data. This will imply that the population model no longer holds for the sample. Pfeffermann and Sverchkov (2007) used the relationships between the population and sample distribution of the study variable to obtain approximately unbiased semi-parametric predictors of the area means under informative sampling schemes. Their procedure is valid for both sampled and non-sampled areas.
Release date: 2020-06-30 - Articles and reports: 12-001-X201900100009Description:
The demand for small area estimates by users of Statistics Canada’s data has been steadily increasing over recent years. In this paper, we provide a summary of procedures that have been incorporated into a SAS based production system for producing official small area estimates at Statistics Canada. This system includes: procedures based on unit or area level models; the incorporation of the sampling design; the ability to smooth the design variance for each small area if an area level model is used; the ability to ensure that the small area estimates add up to reliable higher level estimates; and the development of diagnostic tools to test the adequacy of the model. The production system has been used to produce small area estimates on an experimental basis for several surveys at Statistics Canada that include: the estimation of health characteristics, the estimation of under-coverage in the census, the estimation of manufacturing sales and the estimation of unemployment rates and employment counts for the Labour Force Survey. Some of the diagnostics implemented in the system are illustrated using Labour Force Survey data along with administrative auxiliary data.
Release date: 2019-05-07 - Articles and reports: 11-522-X20050019444Description:
There are several ways to improve data quality. One of them is to re-design and test questionnaires for ongoing surveys. The benefits of questionnaire re-design and testing include improving the accuracy by ensuring the questions collect the required data, as well as decreased response burden.
Release date: 2007-03-02 - 5. Variance estimation in two-phase sampling ArchivedArticles and reports: 11-522-X20030017600Description:
This paper extends the Sen-Yates-Grundy (SYG) variance estimators two-phase sampling designs with stratification at the second phase or both phases. It also develops SYG-type variance estimators of the two-phase regression estimators that make use of the first phase auxiliary data.
Release date: 2005-01-26 - 6. Closing remarks of the Symposium 2002: Modelling Survey Data for Social and Economic Research ArchivedArticles and reports: 11-522-X20020016751Description:
Closing remarks
Release date: 2004-09-13 - 7. Domain estimation using linear regression ArchivedArticles and reports: 12-001-X20040016995Description:
One of the main objectives of a sample survey is the computation of estimates of means and totals for specific domains of interest. Domains are determined either before the survey is carried out (primary domains) or after it has been carried out (secondary domains). The reliability of the associated estimates depends on the variability of the sample size as well as on the y-variables of interest. This variability cannot be controlled in the absence of auxiliary information for subgroups of the population. However, if auxiliary information is available, the estimated reliability of the resulting estimates can be controlled to some extent. In this paper, we study the potential improvements in terms of the reliability of domain estimates that use auxiliary information. The properties (bias, coverage, efficiency) of various estimators that use auxiliary information are compared using a conditional approach.
Release date: 2004-07-14 - 8. Double sampling ArchivedArticles and reports: 12-001-X20010026091Description:
The theory of double sampling is usually presented under the assumption that one of the samples is nested within the other. This type of sampling is called two-phase sampling. The first-phase sample provides auxiliary information (x) that is relatively inexpensive to obtain, whereas the second-phase sample: (b) to improve the estimate using a difference, ratio or regression estimator; or (c) to draw a sub-sample of non-respondent units. However, it is not necessary for one of the samples to be nested in the other or selected from the same frame. The case of non-nested double sampling is dealt with in passing in the classical works on sampling (Des Raj 1968, Cochrane 1977). This method is now used in several national statistical agencies. This paper consolidates double sampling by presenting it in a unified manner. Several examples of surveys used at Statistics Canada illustrate this unification.
Release date: 2002-02-28 - Articles and reports: 12-001-X19980013905Description:
Two-phase sampling designs offer a variety of possibilities for use of auxiliary information. We begin by reviewing the different forms that auxiliary information may take in two-phase surveys. We then set up the procedure by which this information is transformed into calibrated weights, which we use to construct efficient estimators of a population total. The calibration is done in two steps: (i) at the population level; (ii) at the level of the first-phase sample. We go on to show that the resulting calibration estimators are also derivable via regression fitting in two steps. We examine these estimators for a special case of interest, namely, when auxiliary information is available for population subgroups called calibration groups. Postrata are the simplest example of such groups. Estimation for domains of interest and variance estimation are also discussed. These results are illustrated by applying them to two-phase designs at Statistics Canada. The general theory for using auxiliary information in two-phase sampling is being incorporated into Statistics Canada's Generalized Estimation System.
Release date: 1998-07-31 - 10. Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization ArchivedArticles and reports: 12-001-X19960022978Description:
The use of auxiliary information in estimation procedures in complex surveys, such as Statistics Canada's Labour Force Survey, is becoming increasingly sophisticated. In the past, regression and raking ratio estimation were the commonly used procedures for incorporating auxiliary data into the estimation process. However, the weights associated with these estimators could be negative or highly positive. Recent theoretical developments by Deville and Sárndal (1992) in the construction of "restricted" weights, which can be forced to be positive and upwardly bounded, has led us to study the properties of the resulting estimators. In this paper, we investigate the properties of a number of such weight generating procedures, as well as their corresponding estimated variances. In particular, two variance estimation procedures are investigated via a Monte Carlo simulation study based on Labour Force Survey data; they are Jackknifing and Taylor Linearization. The conclusion is that the bias of both the point estimators and the variance estimators is minimal, even under severe "restricting" of the final weights.
Release date: 1997-01-30
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