Small area prediction for a unit-level lognormal model

Berg, Emily; Chandra, Hukum

doi:10.1016/j.csda.2014.03.007

Cited by 30 publications

(58 citation statements)

References 13 publications

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“…When dealing with large enterprises one could expect extremely skewed distributions with outliers. Under these settings, either transformation methods (Berg andChandra 2012 or Shlomo and or robust models should be considered (Sinha andRao 2009 or Chambers andTzavidis 2006). A comparison of robust small area methods including computational issues can be drawn from Schmid (2012).…”

Section: Discussionmentioning

confidence: 99%

The Impact of Sampling Designs on Small Area Estimates for Business Data

Burgard

Münnich

Zimmermann

2014

Journal of Official Statistics

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Evidence-based policy making and economic decision making rely on accurate business information on a national level and increasingly also on smaller regions and business classes. In general, traditional design-based methods suffer from low accuracy in the case of very small sample sizes in certain subgroups, whereas model-based methods, such as small area techniques, heavily rely on strong statistical models.In small area applications in business statistics, two major issues may occur. First, in many countries business registers do not deliver strong auxiliary information for adequate model building. Second, sampling designs in business surveys are generally nonignorable and contain a large variation of survey weights.The present study focuses on the performance of small area point and accuracy estimates of business statistics under different sampling designs. Different strategies of including sampling design information in the models are discussed. A design-based Monte Carlo simulation study unveils the impact of the variability of design weights and different levels of aggregation on model-versus design-based estimation methods. This study is based on a close to reality data set generated from Italian business data.

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Section: Discussionmentioning

confidence: 99%

The Impact of Sampling Designs on Small Area Estimates for Business Data

Burgard

Münnich

Zimmermann

2014

Journal of Official Statistics

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“…Finally, Berg and Chandra () use (1) to develop the empirical version of the minimum mean squared error (MMSE) predictor for

m_{i}

. This is

{\overset{m}{true}}_{i}^{E B P} = N_{i}^{- 1} \{\sum_{s_{i}} y_{i j} + \sum_{r_{i}} {\overset{y}{true}}_{i j}^{E B P}\},

where

{\overset{y}{true}}_{i j}^{E B P} = exp {{boldz}_{i j}^{T} bold-italic \overset{β}{true} + {\overset{γ}{true}}_{i} ({\overset{l}{true}}_{i s} - {boldz}_{i j}^{T} bold-italic \overset{β}{true}) + 0.5 {\overset{σ}{true}}_{e}^{2} (1 + n_{i}^{- 1} {\hat{γ}}_{i})}

.…”

Section: Small Area Estimation Under Transformation To Linearitymentioning

confidence: 99%

“…That is, the MMSE predictor (8) is biased. Berg and Chandra () use Taylor series approximation to bias correct this predictor. Following their development, a bias corrected version of (8) is

{\overset{m}{true}}_{i}^{E B P - B C} = N_{i}^{- 1} \{\sum_{s_{i}} y_{i j} + \sum_{r_{i}} {\overset{y}{true}}_{i j}^{E B P - B C}\},

where

{\overset{y}{true}}_{i j}^{E B P - B C} = {({\overset{c}{true}}_{i j}^{E B P})}^{- 1} {\overset{y}{true}}_{i j}^{E B P}

, with

c_{i j}^{E B P} = exp \{0.5 ({bolda}_{i j} + {\overset{c}{true}}_{i 1} \hat{V} ({\hat{σ}}_{e}^{2}) + {\overset{c}{true}}_{i 2} \hat{V} ({\hat{σ}}_{u}^{2}) + 2 {\overset{c}{true}}_{i 3} \hat{C} o v ({\hat{σ}}_{e}^{2}, {\hat{σ}}_{u}^{2}))\} .

…”

Section: Small Area Estimation Under Transformation To Linearitymentioning

confidence: 99%

“…Balanced against this however is its inherent robustness to misspecification of the model for the y i j . Finally, Berg and Chandra (2012) use (1) to develop the empirical version of the minimum mean squared error (MMSE) predictor for m i . This iŝ…”

Section: Small Area Estimation Under Transformation To Linearitymentioning

confidence: 99%

“…That is, the MMSE predictor (8) is biased. Berg and Chandra (2012) use Taylor series approximation to bias correct this predictor. Following their development, a bias corrected version of (8) iŝ…”

Section: Small Area Estimation Under Transformation To Linearitymentioning

confidence: 99%

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Small area estimation for semicontinuous data

Chandra

Chambers

2014

Biometrical J

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Survey data often contain measurements for variables that are semicontinuous in nature, i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linearmixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the nonzero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a nonzero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale. Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study. Disciplines Engineering | Science and Technology Studies AbstractSurvey data often contain measurements for variables that are semicontinuous in nature,i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linear mixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the non-zero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a non-zero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale.Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study.

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