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• 1. Small area estimation of survey weighted counts under aggregated level spatial model Archived

  Articles and reports: 12-001-X201900100006

  Description:

  The empirical predictor under an area level version of the generalized linear mixed model (GLMM) is extensively used in small area estimation (SAE) for counts. However, this approach does not use the sampling weights or clustering information that are essential for valid inference given the informative samples produced by modern complex survey designs. This paper describes an SAE method that incorporates this sampling information when estimating small area proportions or counts under an area level version of the GLMM. The approach is further extended under a spatial dependent version of the GLMM (SGLMM). The mean squared error (MSE) estimation for this method is also discussed. This SAE method is then applied to estimate the extent of household poverty in different districts of the rural part of the state of Uttar Pradesh in India by linking data from the 2011-12 Household Consumer Expenditure Survey collected by the National Sample Survey Office (NSSO) of India, and the 2011 Indian Population Census. Results from this application indicate a substantial gain in precision for the new methods compared to the direct survey estimates.

  Release date: 2019-05-07

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• 2. On bias-robust mean squared error estimation for pseudo-linear small area estimators Archived

  Articles and reports: 12-001-X201100211604

  Description:

  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

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• 3. Small area estimation under transformation to linearity Archived

  Articles and reports: 12-001-X201100111446

  Description:

  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

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Articles and reports (3) ((3 results))

• 1. Small area estimation of survey weighted counts under aggregated level spatial model Archived

  Articles and reports: 12-001-X201900100006

  Description:

  The empirical predictor under an area level version of the generalized linear mixed model (GLMM) is extensively used in small area estimation (SAE) for counts. However, this approach does not use the sampling weights or clustering information that are essential for valid inference given the informative samples produced by modern complex survey designs. This paper describes an SAE method that incorporates this sampling information when estimating small area proportions or counts under an area level version of the GLMM. The approach is further extended under a spatial dependent version of the GLMM (SGLMM). The mean squared error (MSE) estimation for this method is also discussed. This SAE method is then applied to estimate the extent of household poverty in different districts of the rural part of the state of Uttar Pradesh in India by linking data from the 2011-12 Household Consumer Expenditure Survey collected by the National Sample Survey Office (NSSO) of India, and the 2011 Indian Population Census. Results from this application indicate a substantial gain in precision for the new methods compared to the direct survey estimates.

  Release date: 2019-05-07

  ---

• 2. On bias-robust mean squared error estimation for pseudo-linear small area estimators Archived

  Articles and reports: 12-001-X201100211604

  Description:

  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

  ---

• 3. Small area estimation under transformation to linearity Archived

  Articles and reports: 12-001-X201100111446

  Description:

  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

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