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- 1. Small area estimation under a two-level model ArchivedArticles and reports: 12-001-X200800110612Description:
Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.
Release date: 2008-06-26 - 2. Small area estimation under a restriction ArchivedArticles and reports: 12-001-X200800110619Description:
Small area prediction based on random effects, called EBLUP, is a procedure for constructing estimates for small geographical areas or small subpopulations using existing survey data. The total of the small area predictors is often forced to equal the direct survey estimate and such predictors are said to be calibrated. Several calibrated predictors are reviewed and a criterion that unifies the derivation of these calibrated predictors is presented. The predictor that is the unique best linear unbiased predictor under the criterion is derived and the mean square error of the calibrated predictors is discussed. Implicit in the imposition of the restriction is the possibility that the small area model is misspecified and the predictors are biased. Augmented models with one additional explanatory variable for which the usual small area predictors achieve the self-calibrated property are considered. Simulations demonstrate that calibrated predictors have slightly smaller bias compared to those of the usual EBLUP predictor. However, if the bias is a concern, a better approach is to use an augmented model with an added auxiliary variable that is a function of area size. In the simulation, the predictors based on the augmented model had smaller MSE than EBLUP when the incorrect model was used for prediction. Furthermore, there was a very small increase in MSE relative to EBLUP if the auxiliary variable was added to the correct model.
Release date: 2008-06-26 - 3. Network sampling with a bayesian approach ArchivedArticles and reports: 11-522-X20040018730Description:
This paper considers a link-tracing sampling design. It describes the Bayesian approach for the estimation of social network properties and gives an example.
Release date: 2005-10-27 - Articles and reports: 12-001-X20050018094Description:
Nested error regression models are frequently used in small-area estimation and related problems. Standard regression model selection criterion, when applied to nested error regression models, may result in inefficient model selection methods. We illustrate this point by examining the performance of the C_P statistic through a Monte Carlo simulation study. The inefficiency of the C_P statistic may, however, be rectified by a suitable transformation of the data.
Release date: 2005-07-21 - Articles and reports: 12-001-X20040016991Description:
In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - Articles and reports: 88F0006X1997013Description:
Statistics Canada is engaged in a project "Information System for Science and Technology" which purpose is to develop useful indicators of activity and a framework to tie them together into a coherent picture of science and technology (S&T) in Canada. The Working papers series is used to publish results of the different initiatives conducted within this project. The produced data are related to the activities, linkages and outcomes of S&T. Several key areas are covered such as: innovation, technology diffusion, human resources in S&T and interrelations between different actors involved in S&T. This series also presents important data tabulations taken from regular surveys on R&D and S&T and made possible because of the existing Project.
Release date: 1998-09-25
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Analysis (7) ((7 results))
- 1. Small area estimation under a two-level model ArchivedArticles and reports: 12-001-X200800110612Description:
Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.
Release date: 2008-06-26 - 2. Small area estimation under a restriction ArchivedArticles and reports: 12-001-X200800110619Description:
Small area prediction based on random effects, called EBLUP, is a procedure for constructing estimates for small geographical areas or small subpopulations using existing survey data. The total of the small area predictors is often forced to equal the direct survey estimate and such predictors are said to be calibrated. Several calibrated predictors are reviewed and a criterion that unifies the derivation of these calibrated predictors is presented. The predictor that is the unique best linear unbiased predictor under the criterion is derived and the mean square error of the calibrated predictors is discussed. Implicit in the imposition of the restriction is the possibility that the small area model is misspecified and the predictors are biased. Augmented models with one additional explanatory variable for which the usual small area predictors achieve the self-calibrated property are considered. Simulations demonstrate that calibrated predictors have slightly smaller bias compared to those of the usual EBLUP predictor. However, if the bias is a concern, a better approach is to use an augmented model with an added auxiliary variable that is a function of area size. In the simulation, the predictors based on the augmented model had smaller MSE than EBLUP when the incorrect model was used for prediction. Furthermore, there was a very small increase in MSE relative to EBLUP if the auxiliary variable was added to the correct model.
Release date: 2008-06-26 - 3. Network sampling with a bayesian approach ArchivedArticles and reports: 11-522-X20040018730Description:
This paper considers a link-tracing sampling design. It describes the Bayesian approach for the estimation of social network properties and gives an example.
Release date: 2005-10-27 - Articles and reports: 12-001-X20050018094Description:
Nested error regression models are frequently used in small-area estimation and related problems. Standard regression model selection criterion, when applied to nested error regression models, may result in inefficient model selection methods. We illustrate this point by examining the performance of the C_P statistic through a Monte Carlo simulation study. The inefficiency of the C_P statistic may, however, be rectified by a suitable transformation of the data.
Release date: 2005-07-21 - Articles and reports: 12-001-X20040016991Description:
In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - Articles and reports: 88F0006X1997013Description:
Statistics Canada is engaged in a project "Information System for Science and Technology" which purpose is to develop useful indicators of activity and a framework to tie them together into a coherent picture of science and technology (S&T) in Canada. The Working papers series is used to publish results of the different initiatives conducted within this project. The produced data are related to the activities, linkages and outcomes of S&T. Several key areas are covered such as: innovation, technology diffusion, human resources in S&T and interrelations between different actors involved in S&T. This series also presents important data tabulations taken from regular surveys on R&D and S&T and made possible because of the existing Project.
Release date: 1998-09-25
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