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  • Articles and reports: 12-001-X201800254958
    Description:

    Domains (or subpopulations) with small sample sizes are called small areas. Traditional direct estimators for small areas do not provide adequate precision because the area-specific sample sizes are small. On the other hand, demand for reliable small area statistics has greatly increased. Model-based indirect estimators of small area means or totals are currently used to address difficulties with direct estimation. These estimators are based on linking models that borrow information across areas to increase the efficiency. In particular, empirical best (EB) estimators under area level and unit level linear regression models with random small area effects have received a lot of attention in the literature. Model mean squared error (MSE) of EB estimators is often used to measure the variability of the estimators. Linearization-based estimators of model MSE as well as jackknife and bootstrap estimators are widely used. On the other hand, National Statistical Agencies are often interested in estimating the design MSE of EB estimators in line with traditional design MSE estimators associated with direct estimators for large areas with adequate sample sizes. Estimators of design MSE of EB estimators can be obtained for area level models but they tend to be unstable when the area sample size is small. Composite MSE estimators are proposed in this paper and they are obtained by taking a weighted sum of the design MSE estimator and the model MSE estimator. Properties of the MSE estimators under the area level model are studied in terms of design bias, relative root mean squared error and coverage rate of confidence intervals. The case of a unit level model is also examined under simple random sampling within each area. Results of a simulation study show that the proposed composite MSE estimators provide a good compromise in estimating the design MSE.

    Release date: 2018-12-20

  • Articles and reports: 12-001-X201600114542
    Description:

    The restricted maximum likelihood (REML) method is generally used to estimate the variance of the random area effect under the Fay-Herriot model (Fay and Herriot 1979) to obtain the empirical best linear unbiased (EBLUP) estimator of a small area mean. When the REML estimate is zero, the weight of the direct sample estimator is zero and the EBLUP becomes a synthetic estimator. This is not often desirable. As a solution to this problem, Li and Lahiri (2011) and Yoshimori and Lahiri (2014) developed adjusted maximum likelihood (ADM) consistent variance estimators which always yield positive variance estimates. Some of the ADM estimators always yield positive estimates but they have a large bias and this affects the estimation of the mean squared error (MSE) of the EBLUP. We propose to use a MIX variance estimator, defined as a combination of the REML and ADM methods. We show that it is unbiased up to the second order and it always yields a positive variance estimate. Furthermore, we propose an MSE estimator under the MIX method and show via a model-based simulation that in many situations, it performs better than other ‘Taylor linearization’ MSE estimators proposed recently.

    Release date: 2016-06-22

  • Articles and reports: 12-001-X19990014716
    Description:

    Two design-based estimators of gross flows and transition rates are considered. One makes use of the cross-sectional samples for the estimation of the income class boundaries at each time period and the longitudinal sample for the estimation of counts of units in the longitudinal population (longitudinal counts); this is the mixed estimator. The other one is entirely based on the longitudinal sample, both for the estimation of the class boundaries and the longitudinal counts; this is the longitudinal estimator. We compare the two estimators in the presence of large attrition rates, by means of a simulation. We find that under a less than perfect model of compensation for attrition, the mixed estimator is usually more sensitive to model bias than the longitudinal estimator. Furthermore, we find that for the mixed estimator, the magnitude of this bias overshadows the small gain in precision when compared to the longitudinal estimator. The results are illustrated with data from the Survey of Labour and Income Dynamics and the Longitudinal Administrative Database of Statistics Canada.

    Release date: 1999-10-08

  • Articles and reports: 12-001-X199300214458
    Description:

    In this article we report the results of fitting a state-space model to Canadian unemployment rates. The model assumes an additive decomposition of the population values into a trend, seasonal and irregular component and separate autoregressive relationships for the six survey error series corresponding to the six monthly panel estimators. The model includes rotation group effects and permits the design variances of the survey errors to change over time. The model is fitted at the small area level but it accounts for correlations between the component series of different areas. The robustness of estimators obtained under the model is achieved by imposing the constraint that the monthly aggregate model based estimators in a group of small areas for which the total sample size is sufficiently large coincide with the corresponding direct survey estimators. The performance of the model when fitted to the Atlantic provinces is assessed by a variety of diagnostic statistics and residual plots and by comparisons with estimators in current use.

    Release date: 1993-12-15
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Articles and reports (4)

Articles and reports (4) ((4 results))

  • Articles and reports: 12-001-X201800254958
    Description:

    Domains (or subpopulations) with small sample sizes are called small areas. Traditional direct estimators for small areas do not provide adequate precision because the area-specific sample sizes are small. On the other hand, demand for reliable small area statistics has greatly increased. Model-based indirect estimators of small area means or totals are currently used to address difficulties with direct estimation. These estimators are based on linking models that borrow information across areas to increase the efficiency. In particular, empirical best (EB) estimators under area level and unit level linear regression models with random small area effects have received a lot of attention in the literature. Model mean squared error (MSE) of EB estimators is often used to measure the variability of the estimators. Linearization-based estimators of model MSE as well as jackknife and bootstrap estimators are widely used. On the other hand, National Statistical Agencies are often interested in estimating the design MSE of EB estimators in line with traditional design MSE estimators associated with direct estimators for large areas with adequate sample sizes. Estimators of design MSE of EB estimators can be obtained for area level models but they tend to be unstable when the area sample size is small. Composite MSE estimators are proposed in this paper and they are obtained by taking a weighted sum of the design MSE estimator and the model MSE estimator. Properties of the MSE estimators under the area level model are studied in terms of design bias, relative root mean squared error and coverage rate of confidence intervals. The case of a unit level model is also examined under simple random sampling within each area. Results of a simulation study show that the proposed composite MSE estimators provide a good compromise in estimating the design MSE.

    Release date: 2018-12-20

  • Articles and reports: 12-001-X201600114542
    Description:

    The restricted maximum likelihood (REML) method is generally used to estimate the variance of the random area effect under the Fay-Herriot model (Fay and Herriot 1979) to obtain the empirical best linear unbiased (EBLUP) estimator of a small area mean. When the REML estimate is zero, the weight of the direct sample estimator is zero and the EBLUP becomes a synthetic estimator. This is not often desirable. As a solution to this problem, Li and Lahiri (2011) and Yoshimori and Lahiri (2014) developed adjusted maximum likelihood (ADM) consistent variance estimators which always yield positive variance estimates. Some of the ADM estimators always yield positive estimates but they have a large bias and this affects the estimation of the mean squared error (MSE) of the EBLUP. We propose to use a MIX variance estimator, defined as a combination of the REML and ADM methods. We show that it is unbiased up to the second order and it always yields a positive variance estimate. Furthermore, we propose an MSE estimator under the MIX method and show via a model-based simulation that in many situations, it performs better than other ‘Taylor linearization’ MSE estimators proposed recently.

    Release date: 2016-06-22

  • Articles and reports: 12-001-X19990014716
    Description:

    Two design-based estimators of gross flows and transition rates are considered. One makes use of the cross-sectional samples for the estimation of the income class boundaries at each time period and the longitudinal sample for the estimation of counts of units in the longitudinal population (longitudinal counts); this is the mixed estimator. The other one is entirely based on the longitudinal sample, both for the estimation of the class boundaries and the longitudinal counts; this is the longitudinal estimator. We compare the two estimators in the presence of large attrition rates, by means of a simulation. We find that under a less than perfect model of compensation for attrition, the mixed estimator is usually more sensitive to model bias than the longitudinal estimator. Furthermore, we find that for the mixed estimator, the magnitude of this bias overshadows the small gain in precision when compared to the longitudinal estimator. The results are illustrated with data from the Survey of Labour and Income Dynamics and the Longitudinal Administrative Database of Statistics Canada.

    Release date: 1999-10-08

  • Articles and reports: 12-001-X199300214458
    Description:

    In this article we report the results of fitting a state-space model to Canadian unemployment rates. The model assumes an additive decomposition of the population values into a trend, seasonal and irregular component and separate autoregressive relationships for the six survey error series corresponding to the six monthly panel estimators. The model includes rotation group effects and permits the design variances of the survey errors to change over time. The model is fitted at the small area level but it accounts for correlations between the component series of different areas. The robustness of estimators obtained under the model is achieved by imposing the constraint that the monthly aggregate model based estimators in a group of small areas for which the total sample size is sufficiently large coincide with the corresponding direct survey estimators. The performance of the model when fitted to the Atlantic provinces is assessed by a variety of diagnostic statistics and residual plots and by comparisons with estimators in current use.

    Release date: 1993-12-15
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