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1. Robust estimation of mean squared prediction error in small‐area estimation

   https://doi.org/10.1002/cjs.11567  

   Wu, Ping; Jiang, Jiming (June 2021, Canadian Journal of Statistics)

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2. Empirical Bayes small area prediction under a zero‐inflated lognormal model with correlated random area effects

   https://doi.org/10.1002/bimj.202000029  

   Lyu, Xiaodan; Berg, Emily J.; Hofmann, Heike (July 2020, Biometrical Journal)

   Abstract Many variables of interest in agricultural or economical surveys have skewed distributions and can equal zero. Our data are measures of sheet and rill erosion called Revised Universal Soil Loss Equation‐2 (RUSLE2). Small area estimates of mean RUSLE2 erosion are of interest. We use a zero‐inflated lognormal mixed effects model for small area estimation. The model combines a unit‐level lognormal model for the positive RUSLE2 responses with a unit‐level logistic mixed effects model for the binary indicator that the response is nonzero. In the Conservation Effects Assessment Project (CEAP) data, counties with a higher probability of nonzero responses also tend to have a higher mean among the positive RUSLE2 values. We capture this property of the data through an assumption that the pair of random effects for a county are correlated. We develop empirical Bayes (EB) small area predictors and a bootstrap estimator of the mean squared error (MSE). In simulations, the proposed predictor is superior to simpler alternatives. We then apply the method to construct EB predictors of mean RUSLE2 erosion for South Dakota counties. To obtain auxiliary variables for the population of cropland in South Dakota, we integrate a satellite‐derived land cover map with a geographic database of soil properties. We provide an R Shiny application calledviscover(available athttps://lyux.shinyapps.io/viscover/) to visualize the overlay operations required to construct the covariates. On the basis of bootstrap estimates of the mean square error, we conclude that the EB predictors of mean RUSLE2 erosion are superior to direct estimators. 

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3. Small area prediction of quantiles for zero-inflated data and an informative sample design

   https://doi.org/10.1080/24754269.2019.1666243  

   Berg, Emily; Lee, Danhyang (July 2019, Statistical Theory and Related Fields)
4. Robust Small Area Estimation: An Overview

   https://doi.org/10.1146/annurev-statistics-031219-041212  

   Jiang, J.; Rao, J.S. (April 2020, Annual review of statistics and its application)

   A small area typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. While traditional small area methods and models are widely used nowadays, there have also been much work and interest in robust statistical inference for small area estimation (SAE). We survey this work and provide a comprehensive review here.We begin with a brief review of the traditional SAE methods. We then discuss SAEmethods that are developed under weaker assumptions and SAE methods that are robust in certain ways, such as in terms of outliers or model failure. Our discussion also includes topics such as nonparametric SAE methods, Bayesian approaches, model selection and diagnostics, and missing data. A brief review of software packages available for implementing robust SAE methods is also given. 

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5. An approximate best prediction approach to small area estimation for sheet and rill erosion under informative sampling

   https://doi.org/10.1214/20-AOAS1388  

   Berg, Emily; Kim, Jae-Kwang (March 2021, The Annals of Applied Statistics)

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