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All (5) ((5 results))
- 1. Robust Bayesian small area estimation ArchivedArticles and reports: 12-001-X201800154959Description:
Small area models handling area level data typically assume normality of random effects. This assumption does not always work. The present paper introduces a new small area model with t random effects. Along with this, this paper also considers joint modeling of small area means and variances. The present approach is shown to perform better than other methods.
Release date: 2018-06-21 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X200900211042Description:
This paper proposes an approach for small area prediction based on data obtained from periodic surveys and censuses. We apply our approach to obtain population predictions for the municipalities not sampled in the Brazilian annual Household Survey (PNAD), as well as to increase the precision of the design-based estimates obtained for the sampled municipalities. In addition to the data provided by the PNAD, we use census demographic data from 1991 and 2000, as well as a complete population count conducted in 1996. Hierarchically non-structured and spatially structured growth models that gain strength from all the sampled municipalities are proposed and compared.
Release date: 2009-12-23 - Articles and reports: 12-001-X200800210764Description:
This paper considers situations where the target response value is either zero or an observation from a continuous distribution. A typical example analyzed in the paper is the assessment of literacy proficiency with the possible outcome being either zero, indicating illiteracy, or a positive score measuring the level of literacy. Our interest is in how to obtain valid estimates of the average response, or the proportion of positive responses in small areas, for which only small samples or no samples are available. As in other small area estimation problems, the small sample sizes in at least some of the sampled areas and/or the existence of nonsampled areas requires the use of model based methods. Available methods, however, are not suitable for this kind of data because of the mixed distribution of the responses, having a large peak at zero, juxtaposed to a continuous distribution for the rest of the responses. We develop, therefore, a suitable two-part random effects model and show how to fit the model and assess its goodness of fit, and how to compute the small area estimators of interest and measure their precision. The proposed method is illustrated using simulated data and data obtained from a literacy survey conducted in Cambodia.
Release date: 2008-12-23 - 5. Small area estimation using multilevel models ArchivedArticles and reports: 12-001-X19990014714Description:
In this paper a general multilevel model framework is used to provide estimates for small areas using survey data. This class of models allows for variation between areas because of: (i) differences in the distributions of unit level variables between areas, (ii) differences in the distribution of area level variables between areas (iii) area specific components of variance which make provision for additional local variation which cannot be explained by unit-level or area-level covariates. Small area estimators are derived for this multilevel model formulation and an approximation to the mean square error (MSE) of each small area estimates for this general class of mixed models is provided together with an estimator of this MSE. Both the approximations to the MSE and the estimator of MSE take into account three sources of variation: (i) the prediction MSE assuming that both the fixed and components of variance terms in the multilevel model are knows, (ii) the additional component due to the fact that the fixed coefficients must be estimated, and (iii) the further component due to the fact that the components of variance in the model must be estimated. The proposed methods are estimated using a large data set as a basis for numerical investigation. The results confirm that the extra components of variance contained in multilevel models as well as small area covariates can improve small area estimates and that the MSE approximation and estimator are satisfactory.
Release date: 1999-10-08
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Articles and reports (5)
Articles and reports (5) ((5 results))
- 1. Robust Bayesian small area estimation ArchivedArticles and reports: 12-001-X201800154959Description:
Small area models handling area level data typically assume normality of random effects. This assumption does not always work. The present paper introduces a new small area model with t random effects. Along with this, this paper also considers joint modeling of small area means and variances. The present approach is shown to perform better than other methods.
Release date: 2018-06-21 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X200900211042Description:
This paper proposes an approach for small area prediction based on data obtained from periodic surveys and censuses. We apply our approach to obtain population predictions for the municipalities not sampled in the Brazilian annual Household Survey (PNAD), as well as to increase the precision of the design-based estimates obtained for the sampled municipalities. In addition to the data provided by the PNAD, we use census demographic data from 1991 and 2000, as well as a complete population count conducted in 1996. Hierarchically non-structured and spatially structured growth models that gain strength from all the sampled municipalities are proposed and compared.
Release date: 2009-12-23 - Articles and reports: 12-001-X200800210764Description:
This paper considers situations where the target response value is either zero or an observation from a continuous distribution. A typical example analyzed in the paper is the assessment of literacy proficiency with the possible outcome being either zero, indicating illiteracy, or a positive score measuring the level of literacy. Our interest is in how to obtain valid estimates of the average response, or the proportion of positive responses in small areas, for which only small samples or no samples are available. As in other small area estimation problems, the small sample sizes in at least some of the sampled areas and/or the existence of nonsampled areas requires the use of model based methods. Available methods, however, are not suitable for this kind of data because of the mixed distribution of the responses, having a large peak at zero, juxtaposed to a continuous distribution for the rest of the responses. We develop, therefore, a suitable two-part random effects model and show how to fit the model and assess its goodness of fit, and how to compute the small area estimators of interest and measure their precision. The proposed method is illustrated using simulated data and data obtained from a literacy survey conducted in Cambodia.
Release date: 2008-12-23 - 5. Small area estimation using multilevel models ArchivedArticles and reports: 12-001-X19990014714Description:
In this paper a general multilevel model framework is used to provide estimates for small areas using survey data. This class of models allows for variation between areas because of: (i) differences in the distributions of unit level variables between areas, (ii) differences in the distribution of area level variables between areas (iii) area specific components of variance which make provision for additional local variation which cannot be explained by unit-level or area-level covariates. Small area estimators are derived for this multilevel model formulation and an approximation to the mean square error (MSE) of each small area estimates for this general class of mixed models is provided together with an estimator of this MSE. Both the approximations to the MSE and the estimator of MSE take into account three sources of variation: (i) the prediction MSE assuming that both the fixed and components of variance terms in the multilevel model are knows, (ii) the additional component due to the fact that the fixed coefficients must be estimated, and (iii) the further component due to the fact that the components of variance in the model must be estimated. The proposed methods are estimated using a large data set as a basis for numerical investigation. The results confirm that the extra components of variance contained in multilevel models as well as small area covariates can improve small area estimates and that the MSE approximation and estimator are satisfactory.
Release date: 1999-10-08
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