Weighting and estimation
Results
All (7)
All (7) ((7 results))
- Articles and reports: 12-001-X201100211604Description:
We propose a method of mean squared error (MSE) estimation for estimators of finite population domain means that can be expressed in pseudo-linear form, i.e., as weighted sums of sample values. In particular, it can be used for estimating the MSE of the empirical best linear unbiased predictor, the model-based direct estimator and the M-quantile predictor. The proposed method represents an extension of the ideas in Royall and Cumberland (1978) and leads to MSE estimators that are simpler to implement, and potentially more bias-robust, than those suggested in the small area literature. However, it should be noted that the MSE estimators defined using this method can also exhibit large variability when the area-specific sample sizes are very small. We illustrate the performance of the method through extensive model-based and design-based simulation, with the latter based on two realistic survey data sets containing small area information.
Release date: 2011-12-21 - Articles and reports: 12-001-X201100211609Description:
This paper presents a review and assessment of the use of balanced sampling by means of the cube method. After defining the notion of balanced sample and balanced sampling, a short history of the concept of balancing is presented. The theory of the cube method is briefly presented. Emphasis is placed on the practical problems posed by balanced sampling: the interest of the method with respect to other sampling methods and calibration, the field of application, the accuracy of balancing, the choice of auxiliary variables and ways to implement the method.
Release date: 2011-12-21 - 3. Maximum likelihood estimation for contingency tables and logistic regression with incorrectly linked data ArchivedArticles and reports: 12-001-X201100111444Description:
Data linkage is the act of bringing together records that are believed to belong to the same unit (e.g., person or business) from two or more files. It is a very common way to enhance dimensions such as time and breadth or depth of detail. Data linkage is often not an error-free process and can lead to linking a pair of records that do not belong to the same unit. There is an explosion of record linkage applications, yet there has been little work on assuring the quality of analyses using such linked files. Naively treating such a linked file as if it were linked without errors will, in general, lead to biased estimates. This paper develops a maximum likelihood estimator for contingency tables and logistic regression with incorrectly linked records. The estimation technique is simple and is implemented using the well-known EM algorithm. A well known method of linking records in the present context is probabilistic data linking. The paper demonstrates the effectiveness of the proposed estimators in an empirical study which uses probabilistic data linkage.
Release date: 2011-06-29 - 4. Hierarchical Bayes small area estimation under a spatial model with application to health survey data ArchivedArticles and reports: 12-001-X201100111445Description:
In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111446Description:
Small area estimation based on linear mixed models can be inefficient when the underlying relationships are non-linear. In this paper we introduce SAE techniques for variables that can be modelled linearly following a non-linear transformation. In particular, we extend the model-based direct estimator of Chandra and Chambers (2005, 2009) to data that are consistent with a linear mixed model in the logarithmic scale, using model calibration to define appropriate weights for use in this estimator. Our results show that the resulting transformation-based estimator is both efficient and robust with respect to the distribution of the random effects in the model. An application to business survey data demonstrates the satisfactory performance of the method.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111448Description:
In two-phase sampling for stratification, the second-phase sample is selected by a stratified sample based on the information observed in the first-phase sample. We develop a replication-based bias adjusted variance estimator that extends the method of Kim, Navarro and Fuller (2006). The proposed method is also applicable when the first-phase sampling rate is not negligible and when second-phase sample selection is unequal probability Poisson sampling within each stratum. The proposed method can be extended to variance estimation for two-phase regression estimators. Results from a limited simulation study are presented.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111450Description:
This paper examines the efficiency of the Horvitz-Thompson estimator from a systematic probability proportional to size (PPS) sample drawn from a randomly ordered list. In particular, the efficiency is compared with that of an ordinary ratio estimator. The theoretical results are confirmed empirically with of a simulation study using Dutch data from the Producer Price Index.
Release date: 2011-06-29
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Analysis (7)
Analysis (7) ((7 results))
- Articles and reports: 12-001-X201100211604Description:
We propose a method of mean squared error (MSE) estimation for estimators of finite population domain means that can be expressed in pseudo-linear form, i.e., as weighted sums of sample values. In particular, it can be used for estimating the MSE of the empirical best linear unbiased predictor, the model-based direct estimator and the M-quantile predictor. The proposed method represents an extension of the ideas in Royall and Cumberland (1978) and leads to MSE estimators that are simpler to implement, and potentially more bias-robust, than those suggested in the small area literature. However, it should be noted that the MSE estimators defined using this method can also exhibit large variability when the area-specific sample sizes are very small. We illustrate the performance of the method through extensive model-based and design-based simulation, with the latter based on two realistic survey data sets containing small area information.
Release date: 2011-12-21 - Articles and reports: 12-001-X201100211609Description:
This paper presents a review and assessment of the use of balanced sampling by means of the cube method. After defining the notion of balanced sample and balanced sampling, a short history of the concept of balancing is presented. The theory of the cube method is briefly presented. Emphasis is placed on the practical problems posed by balanced sampling: the interest of the method with respect to other sampling methods and calibration, the field of application, the accuracy of balancing, the choice of auxiliary variables and ways to implement the method.
Release date: 2011-12-21 - 3. Maximum likelihood estimation for contingency tables and logistic regression with incorrectly linked data ArchivedArticles and reports: 12-001-X201100111444Description:
Data linkage is the act of bringing together records that are believed to belong to the same unit (e.g., person or business) from two or more files. It is a very common way to enhance dimensions such as time and breadth or depth of detail. Data linkage is often not an error-free process and can lead to linking a pair of records that do not belong to the same unit. There is an explosion of record linkage applications, yet there has been little work on assuring the quality of analyses using such linked files. Naively treating such a linked file as if it were linked without errors will, in general, lead to biased estimates. This paper develops a maximum likelihood estimator for contingency tables and logistic regression with incorrectly linked records. The estimation technique is simple and is implemented using the well-known EM algorithm. A well known method of linking records in the present context is probabilistic data linking. The paper demonstrates the effectiveness of the proposed estimators in an empirical study which uses probabilistic data linkage.
Release date: 2011-06-29 - 4. Hierarchical Bayes small area estimation under a spatial model with application to health survey data ArchivedArticles and reports: 12-001-X201100111445Description:
In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111446Description:
Small area estimation based on linear mixed models can be inefficient when the underlying relationships are non-linear. In this paper we introduce SAE techniques for variables that can be modelled linearly following a non-linear transformation. In particular, we extend the model-based direct estimator of Chandra and Chambers (2005, 2009) to data that are consistent with a linear mixed model in the logarithmic scale, using model calibration to define appropriate weights for use in this estimator. Our results show that the resulting transformation-based estimator is both efficient and robust with respect to the distribution of the random effects in the model. An application to business survey data demonstrates the satisfactory performance of the method.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111448Description:
In two-phase sampling for stratification, the second-phase sample is selected by a stratified sample based on the information observed in the first-phase sample. We develop a replication-based bias adjusted variance estimator that extends the method of Kim, Navarro and Fuller (2006). The proposed method is also applicable when the first-phase sampling rate is not negligible and when second-phase sample selection is unequal probability Poisson sampling within each stratum. The proposed method can be extended to variance estimation for two-phase regression estimators. Results from a limited simulation study are presented.
Release date: 2011-06-29 - Articles and reports: 12-001-X201100111450Description:
This paper examines the efficiency of the Horvitz-Thompson estimator from a systematic probability proportional to size (PPS) sample drawn from a randomly ordered list. In particular, the efficiency is compared with that of an ordinary ratio estimator. The theoretical results are confirmed empirically with of a simulation study using Dutch data from the Producer Price Index.
Release date: 2011-06-29
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