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Parametric transformed Fay–Herriot model for small area estimation

Shonosuke Sugasawa, Tatsuya Kubokawa
2015 Journal of Multivariate Analysis  
In this paper, we consider parametric transformed Fay-Herriot models, and clarify conditions on transformations under which the estimator of the transformation is consistent.  ...  Based on asymptotic properties for estimators of parameters, we derive a second-order approximation of the prediction error of the empirical best linear unbiased predictors (EBLUP) and obtain a second-order  ...  Research of the second author was supported in part by Grant-in-Aid for Scientific Research (21540114 and 23243039) from Japan Society for the Promotion of Science.  ... 
doi:10.1016/j.jmva.2015.04.001 fatcat:dn3bq2pbbvcz3k2ratpszdw464

Small Area Estimation with Uncertain Random Effects

Gauri Sankar Datta, Abhyuday Mandal
2015 Figshare  
Random effects models play an important role in model-based small area estimation.  ...  We empirically evaluated the accuracy of the direct estimates and the estimates obtained from our mixture model and the Fay-Herriot random effects [...]  ...  Plot of ratio of uncertainty measures of various model-based estimates of small area means  ... 
doi:10.6084/m9.figshare.1378720.v1 fatcat:xlqqvohypzau7k6rr2uetq4wam

Transforming response values in small area prediction [article]

Shonosuke Sugasawa, Tatsuya Kubokawa
2017 arXiv   pre-print
The use of a parametric transformation for positive response values in the Fay-Herriot model is proposed for such a case.  ...  An asymptotically unbiased small area predictor is derived and a second-order unbiased estimator of the mean squared error is established using the parametric bootstrap.  ...  Acknowledgement We would like to thank the Associate Editor and the four reviewers for many valuable comments and helpful suggestions which led to an improved version of this paper.  ... 
arXiv:1509.03951v5 fatcat:4rmrkfgj6vbkfmt2kmmjvkddyy

Compound decision in the presence of proxies

Noam Cohen, Eitan Greenshtein, Ya'acov Ritov
2013 Statistica sinica  
We also compare it numerically with Fay-Herriot and other methods, in a real data situation, where the goal is to estimate certain proportions in many small areas (Statistical-Areas).  ...  However, apart from literature in small area estimation, e.g., Rao (2003), which follows the seminal paper of Fay and Herriot (1979), EB is hardly used in modern data analysis.  ...  A different parametric EB approach for estimating proportions in small areas, that involves a logistic regression model, may be found in Farell, et.al.  ... 
doi:10.5705/ss.2011.071 fatcat:rajnqc2njbajxjzqmg7jgi5g6m

Robust estimation of wages in small enterprises: the application to Poland's districts

Grażyna Dehnel, Łukasz Wawrowski
2020 Statistics in Transition New Series  
The aim of the study is to apply a robust version of the Fay-Herriot model to the estimation of average wages in the small business sector.  ...  Moreover, the use of this version of the Fay-Herriot model helps to improve the precision of estimates, especially in domains where samples are of small sizes.  ...  For the Horvitz-Thompson estimator, one can employ the standard replication weights procedure, whereas for the Fay-Herriot and robust Fay-Herriot models, the recommended option is parametric bootstrap  ... 
doi:10.21307/stattrans-2020-008 fatcat:nh4jpoahozdy7lhrtthecfmi4y

Compound decision in the presence of proxies with an application to spatio-temporal data [article]

N. Cohen, E. Greenshtein, Y. Ritov
2010 arXiv   pre-print
We also compare it numerically with Fay-Herriot and other methods, using a 'semi-real' data set that involves spatio-temporal covariates, where the goal is to estimate certain proportions in many small  ...  We suggest a method that involves non-parametric empirical Bayes techniques and may be viewed as a generalization of the celebrated Fay-Herriot (1979) method.  ...  A different parametric EB approach for estimating proportions in small areas, that involves a logistic regression model, may be found in Farell, et.al.  ... 
arXiv:1012.1563v1 fatcat:efiw7zgdgjdbzf3ehd4deb27uq

On the Simulation Study of Jackknife and Bootstrap MSE Estimators of a Domain Mean Predictor for Fay-Herriot Model

2017 Acta Universitatis Lodziensis. Folia Oeconomica  
In the standard Fay-Herriot model the independence of random effects is assumed, and the biases of the MSE estimators are small for large number of domains.  ...  We consider the problem of the estimation of the mean squared error (MSE) of some domain mean predictor for Fay-Herriot model.  ...  under transformed Fay-Herriot model.  ... 
doi:10.18778/0208-6018.331.11 fatcat:qppagangbvek7nrmy5ckjl7cvm

Mean-squared error estimation in transformed Fay-Herriot models

Eric V. Slud, Tapabrata Maiti
2006 Journal of The Royal Statistical Society Series B-statistical Methodology  
The problem of accurately estimating the mean-squared error of small area estimators within a Fay-Herriot normal error model is studied theoretically in the common setting where the model is fitted to  ...  For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the  ...  We are grateful to Bill Bell for useful conversations regarding methodological issues in the SAIPE project and to the referees for suggestions which improved the presentation.  ... 
doi:10.1111/j.1467-9868.2006.00542.x fatcat:erf7nno6dvc3tlivtol2nogxzi

Multivariate Fay–Herriot models for small area estimation

Roberto Benavent, Domingo Morales
2016 Computational Statistics & Data Analysis  
Multivariate Fay-Herriot models for estimating small area indicators are introduced.  ...  Among the available procedures for fitting linear mixed models, the residual maximum likelihood (REML) is employed. The empirical best predictor (EBLUP) of the vector of area means is derived.  ...  The authors also thank the Instituto Nacional de Estadística for providing the Spanish EU-SILC data.  ... 
doi:10.1016/j.csda.2015.07.013 fatcat:dchmsvhtcbaizpzd5ourqdhar4

Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation

M. Ghosh, T. Kubokawa, Y. Kawakubo
2015 Biometrika  
In this paper, we consider the transformed Fay-Herriot model as a multiplicative model for estimating positive small area means, and suggest a weighted Kullback-Leibler divergence as a loss function.  ...  A simple example will be estimation of per capita income for small areas. It is now well-understood that small area estimation needs explicit, or at least implicit use of models.  ...  from Japan Society for the Promotion of Science.  ... 
doi:10.1093/biomet/asv010 fatcat:z5jupnrhmvcnlpe2gycoj24onm

A New Model Variance Estimator for an Area Level Small Area Model to Solve Multiple Problems Simultaneously [article]

Masayo Yoshimori Hirose, Partha Lahiri
2017 arXiv   pre-print
The two-level normal hierarchical model (NHM) has played a critical role in the theory of small area estimation (SAE), one of the growing areas in statistics with numerous applications in different disciplines  ...  The idea of achieving multiple desirable properties in an EBLUP method through a suitably devised model variance estimator is the first of its kind and holds promise in providing good inferences for small  ...  Acknowledgement The first author's research was supported by Grant-in-Aid for Research Activity start-up, JSPS Grant Number 26880011.  ... 
arXiv:1701.04176v1 fatcat:s4zyis54grealjm6drjn7fnhjq

An application of a small area procedure with correlation between measurement error and sampling error to the Conservation Effects Assessment Project [article]

Emily Berg, Sepideh Mosaferi
2021 arXiv   pre-print
We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model for sheet and rill erosion.  ...  As a result of small county sample sizes, small area estimation procedures are needed. One variable that is related to sheet and rill erosion is the quantity of water runoff.  ...  Importantly, the MSPE estimator for the Fay-Herriot model has a severe negative bias for the MSPE of the predictor.  ... 
arXiv:2110.10272v1 fatcat:ejhcuwkmv5dw7b4vtyqrg4iigq

Small area estimates of the low work intensity indicator at voivodeship level in Poland

Łukasz Wawrowski, Maciej Beręsewicz
2021 Statistics in Transition New Series  
However, it is impossible to obtain reliable direct estimates of labour market statistics at low levels based on the EU-SILC survey. In such cases, modelbased small area estimation can be used.  ...  The You (1994), Fay and Diallo (2012) , and Marhuenda, Molina and Morales (2013) models were applied. The bootstrap MSE for the discussed methods was proposed.  ...  Notation for estimators and diagnostics The classic Fay and Herriot (1979) area-level model does not take into account temporal nor spatial random effects.  ... 
doi:10.21307/stattrans-2021-021 fatcat:oyfpu6mvnbapbowdgut3tjyete

Bayesian semiparametric hierarchical empirical likelihood spatial models

Aaron T. Porter, Scott H. Holan, Christopher K. Wikle
2015 Journal of Statistical Planning and Inference  
One of the key tools for small area estimation is the Fay-Herriot (FH) model, due to Fay and Herriot (1979) .  ...  Small area estimation (SAE) is a set of statistical methods to improve the precision of undersampled (unsampled) geographies. For undersampled (unsampled), such as smaller geographies, SAE is needed.  ...  The SHEL model provides a 13% reduction in MSPE over the parametric FH model explicitly accounting for spatial correlation. Explicitly accounting for spatial correlation is key for these data.  ... 
doi:10.1016/j.jspi.2015.04.002 fatcat:sdft7bhknjbe3hyuxmtxfhrvoe

Small-area estimation based on survey data from a left-censored Fay–Herriot model

Eric V. Slud, Tapabrata Maiti
2011 Journal of Statistical Planning and Inference  
We study Small Area Estimation based on data obtained by leftcensored responses from a Fay-Herriot (1979) normal-error model.  ...  The problem is motivated by the Census Bureau's ongoing Small Area Income and Poverty Estimation (SAIPE) project, where a FH model is fitted to a logarithmically transformed response variable (count of  ...  We thank Nancy Kirkendall of EIA for bringing the DOE left-censored surveys to our attention.  ... 
doi:10.1016/j.jspi.2011.05.005 fatcat:eh2shjkpibec7lusozepkwnqja
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