Estimation of Proportions in Small Areas: Application to the Labour Force Using the Swiss Census Structural Survey

Molina, Isabel; Strzałkowska-Kominiak, Ewa

doi:10.1111/rssa.12498

Cited by 16 publications

(34 citation statements)

References 31 publications

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“…For some models, like in (12) below, the covariates x i j need to be known for every unit in the area, and not just for sampled units. Molina and Strzalkowska‐Kominiak () consider the case of a binary response, y i j ∈ {0,1}, and assume the generalised linear mixed model

y_{i j} false| p_{i j} \sim Bernoulli false(p_{i j} false); logit false(p_{i j} false) = x_{i j}^{'} β + u_{i}, u_{i} \sim N false(0, σ_{u}^{2} false) .

…”

Section: Literature Reviewmentioning

confidence: 99%

“…The third estimator considered by Molina and Strzalkowska‐Kominiak () is a ‘parametric design bootstrap estimator’, obtained by generating a (single) population

({}, ((), y_{i j}^{p b}, x_{i j}), i = 1, ⋯, m, j = 1, ⋯, N_{i})

under the model with estimated parameters

\overset{β}{true}, {\overset{σ}{true}}_{u}^{2}

obtained from the original sample, drawing bootstrap samples as under the first method and computing the model‐based predictors

{\overset{P}{true}}_{i, b}^{P B}

for each bootstrap sample and the regression estimators

{\overset{P}{true}}_{i}^{r e g} = {\overset{y}{true}}_{i} + {({\overset{X}{true}}_{i} - {\overset{x}{true}}_{i})}^{'} \hat{β}

based on the original sample for each area, where

false({\overset{y}{true}}_{i}, {\overset{x}{true}}_{i} false) = ((), \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} y_{i j}, \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} x_{i j})

are the sample means and

{\overset{X}{true}}_{i} = \frac{1}{N_{i}} \sum_{j = 1}^{N_{i}} x_{i j}

is the true area mean in area i . The DMSE estimator is defined as

D \overset{M}{true} S E_{P D} false({\overset{P}{true}}_{i} false) = {\overset{γ}{true}}_{i} \frac{1}{B} \sum_{b = 1}^{B} ((), \overset{P}{true})

…”

Section: Literature Reviewmentioning

confidence: 99%

“…Molina and Strzalkowska‐Kominiak () conclude, based on a simulation experiment, that the composite estimator and the parametric design bootstrap estimator have an acceptable quality for estimation of the DMSE of the empirical best linear unbiased predictor (EBLUP)

{\overset{P}{true}}_{i}

under the model .…”

Section: Literature Reviewmentioning

confidence: 99%

“…Unit-level models are applicable for the case where individual observations, y ij ; x ij ; j D 1; : : : ; n i , are available for every sampled area i D 1; : : : ; m. For some models, like in (12) below, the covariates x ij need to be known for every unit in the area, and not just for sampled units. Molina and Strzalkowska-Kominiak (2017) consider the case of a binary response, y ij 2 ¹0; 1º, and assume the generalised linear mixed model…”

Section: Unit-level Modelsmentioning

confidence: 99%

“…As mentioned earlier, we are not aware of any attempt to estimate the DMSE for this, much more complicated model. Molina and Strzalkowska-Kominiak (2017) approximate the mixed logistic model by the mixed linear model. We considered therefore the following DMSE estimators.…”

Section: Simulation Set-up and Estimation Of Target Proportionsmentioning

confidence: 99%

See 4 more Smart Citations

Estimation of Randomisation Mean Square Error in Small Area Estimation

Pfeffermann

Ben‐Hur²

2018

Int Statistical Rev

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Summary In this article, we propose a new method for estimating the randomisation (design‐based) mean squared error (DMSE) of model‐dependent small area predictors. Analogously to classical survey sampling theory, the DMSE considers the finite population values as fixed numbers and accounts for the MSE of small area predictors over all possible sample selections. The proposed method models the true DMSE as computed for synthetic populations and samples drawn from them, as a function of known statistics and then applies the model to the original sample. Several simulation studies for the linear area‐level model and the unit‐level mixed logistic model illustrate the performance of the proposed method and compare it with the performance of other DMSE estimators proposed in the literature.

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y_{i j} false| p_{i j} \sim Bernoulli false(p_{i j} false); logit false(p_{i j} false) = x_{i j}^{'} β + u_{i}, u_{i} \sim N false(0, σ_{u}^{2} false) .

…”

Section: Literature Reviewmentioning

confidence: 99%

“…The third estimator considered by Molina and Strzalkowska‐Kominiak () is a ‘parametric design bootstrap estimator’, obtained by generating a (single) population

({}, ((), y_{i j}^{p b}, x_{i j}), i = 1, ⋯, m, j = 1, ⋯, N_{i})

under the model with estimated parameters

\overset{β}{true}, {\overset{σ}{true}}_{u}^{2}

obtained from the original sample, drawing bootstrap samples as under the first method and computing the model‐based predictors

{\overset{P}{true}}_{i, b}^{P B}

for each bootstrap sample and the regression estimators

{\overset{P}{true}}_{i}^{r e g} = {\overset{y}{true}}_{i} + {({\overset{X}{true}}_{i} - {\overset{x}{true}}_{i})}^{'} \hat{β}

based on the original sample for each area, where

false({\overset{y}{true}}_{i}, {\overset{x}{true}}_{i} false) = ((), \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} y_{i j}, \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} x_{i j})

are the sample means and

{\overset{X}{true}}_{i} = \frac{1}{N_{i}} \sum_{j = 1}^{N_{i}} x_{i j}

is the true area mean in area i . The DMSE estimator is defined as

D \overset{M}{true} S E_{P D} false({\overset{P}{true}}_{i} false) = {\overset{γ}{true}}_{i} \frac{1}{B} \sum_{b = 1}^{B} ((), \overset{P}{true})

…”

Section: Literature Reviewmentioning

confidence: 99%

{\overset{P}{true}}_{i}

under the model .…”

Section: Literature Reviewmentioning

confidence: 99%

Section: Unit-level Modelsmentioning

confidence: 99%

Section: Simulation Set-up and Estimation Of Target Proportionsmentioning

confidence: 99%

See 3 more Smart Citations

Estimation of Randomisation Mean Square Error in Small Area Estimation

Pfeffermann

Ben‐Hur²

2018

Int Statistical Rev

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Estimation of design‐based mean squared error of a small area mean model‐based estimator under a nested error linear regression model

Stefan

Hidiroglou

2021

Can J Statistics

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In this article, we propose a conditional model estimator (cmmse) for the design‐based mean squared error (dMSE) of a small area mean estimator under the basic unit level model. The mean squared error dMSE refers to the variability of a small area estimator over all possible sample selections. It is different from the model mean squared error (mMSE), traditionally used to measure the efficiency in small area estimation problems. For known model parameters, Rao, Rubin‐Bleuer & Estevao [Rao et al., Survey Methodology 2018; 44, 151–166] showed that dMSE depends on two quadratic finite population parameters. A design estimator of dMSE, denoted as dmse, is obtained by substituting the quadratic parameters with their corresponding design unbiased estimators. Rao, Rubin‐Bleuer & Estevao [Rao et al., Survey Methodology 2018; 44, 151–166] proposed a composite MSE estimator (cmse) based on both the design and the model. This estimator is defined as a weighted average between the design‐based dmse and a model‐based estimator (mmse). Given known variance components, we obtain a new formula for dMSE that accounts for the estimation of the fixed model coefficients. Our conditional model MSE estimator cmmse is obtained by replacing the quadratic finite population parameters by their best predictions under the model, in the new formula of dMSE. Properties of the proposed estimator are studied in terms of design bias, relative root mean squared error, coverage rate and a score function of the confidence intervals.

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Estimating regional unemployment with mobile network data for Functional Urban Areas in Germany

Hadam,

Würz,

Kreutzmann

et al. 2023

Stat Methods Appl

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The ongoing growth of cities due to better job opportunities is leading to increased labour-related commuter flows in several countries. On the one hand, an increasing number of people commute and move to the cities, but on the other hand, the labour market indicates higher unemployment rates in urban areas than in the surrounding areas. We investigate this phenomenon on regional level by an alternative definition of unemployment rates in which commuting behaviour is integrated. We combine data from the Labour Force Survey with dynamic mobile network data by small area models for the federal state North Rhine-Westphalia in Germany. From a methodical perspective, we use a transformed Fay–Herriot model with bias correction for the estimation of unemployment rates and propose a parametric bootstrap for the mean squared error estimation that includes the bias correction. The performance of the proposed methodology is evaluated in a case study based on official data and in model-based simulations. The results in the application show that unemployment rates (adjusted by commuters) in German cities are lower than traditional official unemployment rates indicate.

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Estimation of Proportions in Small Areas: Application to the Labour Force Using the Swiss Census Structural Survey

Cited by 16 publications

References 31 publications

Estimation of Randomisation Mean Square Error in Small Area Estimation

Estimation of Randomisation Mean Square Error in Small Area Estimation

Estimation of design‐based mean squared error of a small area mean model‐based estimator under a nested error linear regression model

Estimating regional unemployment with mobile network data for Functional Urban Areas in Germany

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