Small area estimation under spatial nonstationarity

Chandra, Hukum; Salvati, Nicola; Chambers, Ray; Tzavidis, Nikos

doi:10.1016/j.csda.2012.02.006

Cited by 47 publications

(59 citation statements)

References 26 publications

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“…A synthetic population could be also obtained by resampling with replacement from the original data set (see for example Chandra et al . ()), but we prefer to avoid replication of units.…”

Section: Simulation Experimentsmentioning

confidence: 99%

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

Molina

Strzałkowska-Kominiak

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary The main objectives of this paper are to find efficient but computationally simple estimators for the proportions of people in the labour force (economic activity rates) in Swiss communes and to estimate their mean‐squared error (MSE) over the sampling replication mechanism (the design MSE). This will be done by combining survey data with administrative data provided by the Swiss Federal Statistical Office. We find estimators with considerably greater efficiency than currently used direct estimators and that are easy to implement. We show that, under a generalized linear mixed model with logit link, the computationally expensive empirical best predictor does not perform appreciably better than a plug‐in estimator. Moreover, for moderate proportions of active workers, the empirical best linear unbiased predictor (EBLUP) based on a much simpler linear mixed model performs similarly to the above estimators. We propose new bootstrap estimators of the design MSE of the EBLUPs, which ‘borrow strength’ similarly to EBLUPs. Realistic simulation studies carried out under both model‐ and design‐based set‐ups indicate great gains in efficiency of the selected small area estimators over the traditional direct estimators and acceptable performance of the proposed bootstrap MSE estimators. In the application using the Swiss data, coefficient‐of‐variation reductions of the estimates obtained for the communes are remarkable.

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“…A synthetic population could be also obtained by resampling with replacement from the original data set (see for example Chandra et al . ()), but we prefer to avoid replication of units.…”

Section: Simulation Experimentsmentioning

confidence: 99%

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

Molina

Strzałkowska-Kominiak

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…Here

{\overset{γ}{true}}_{i} = {\overset{σ}{true}}_{u}^{2} {({\overset{σ}{true}}_{u}^{2} + n_{i}^{- 1} {\overset{σ}{true}}_{e}^{2})}^{- 1}

is the plug‐in estimator of the shrinkage effect

γ_{i} = σ_{u}^{2} {(σ_{u}^{2} + n_{i}^{- 1} σ_{e}^{2})}^{- 1}

, and

{\overset{l}{true}}_{i s} = n_{i}^{- 1} \sum_{j \in s_{i}} prefixlog (y_{i j})

and

{\bar{normalz}}_{i s} = n_{i}^{- 1} \sum_{j \in s_{i}} {boldz}_{i j}

are the sample means of

l_{i j}

and

z_{i j}

, respectively, in area i . Using a prediction‐based approach similar to that described in Karlberg (), Chandra and Chambers () then propose a synthetic type predictor for the area mean

m_{i}

under model (1) of the form

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

where

{\overset{y}{true}}_{i j}^{S Y N - E P} = {((), {\overset{c}{true}}_{i j}^{S Y N - E P})}^{-}

…”

Section: Small Area Estimation Under Transformation To Linearitymentioning

confidence: 99%

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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“…Its popularity as a research topic is spawning a wide range of spatial model specifications, from geographically weighted regression (e.g., Chandra et al 2012;Salvati et al 2012), through spatial autoregressive (e.g., Griffith, Haining, and Bennett 1989;Petrucci, Pratesi, and Salvati 2005), to space-time (e.g., Singh, Shukla, and Kundu 2005;Pereira and Coelho 2012). Its popularity as a research topic is spawning a wide range of spatial model specifications, from geographically weighted regression (e.g., Chandra et al 2012;Salvati et al 2012), through spatial autoregressive (e.g., Griffith, Haining, and Bennett 1989;Petrucci, Pratesi, and Salvati 2005), to space-time (e.g., Singh, Shukla, and Kundu 2005;Pereira and Coelho 2012).…”

Section: Small Geographic Area Estimationmentioning

confidence: 99%

Estimating Missing Data Values for GeoreferencedPoisson Counts

Griffith

2013

Geographical Analysis

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Empirical scientists often are faced with incomplete data and desire imputations for their missing data values. The expectation–maximization algorithm is a generic tool that offers maximum likelihood solutions for such data sets. This article pursues this type of solution for Poisson random variables, utilizing a generalized linear model extension that mirrors the linear analysis of a covariance regression specification. This formulation allows a mixed model to be implemented and contrasted with a Poisson‐gamma mixture (i.e., negative binomial) model. Simple comparisons are made between model specification results for a population counts example, with and without a constraint on the total of the missing counts. 实证研究常面临数据缺失问题，需要相应的数据插补方法。最大期望算法（EM）为此类数据集进行最大似然求解提供了通用工具。本文通过提出一个可包含线性协方差回归(ANCOVA)等在内的扩展广义线性模型，将该类解决方案拓展到泊松随机变量。该方法允许建立混合模型，并可与泊松‐伽玛混合模型（即负二项式）对比。以人口计数为案例对有无缺失数据条件下模型的设定与结果进行了简要的对比。

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Small area estimation under spatial nonstationarity

Cited by 47 publications

References 26 publications

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

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

Small area estimation for semicontinuous data

Estimating Missing Data Values for GeoreferencedPoisson Counts

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