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Crop statistics for a small area, such as the community development block, are an increasingly important topic in agricultural statistics. Under normality assumptions, the classic Empirical Best Linear Unbiased Prediction (EBLUP) technique is effective for predicting small area means, however the Small Area Estimation (SAE) model can be heavily affected by the incidence of outliers or deviations from the expected distribution. The purpose of this study was to estimate variance, predict block-level wheat crop yield in the Hisar and Sirsa district of Haryana by classical SAE method and a robust random-effect predictor using a slight generalization of Huber's Proposal 2. In the case of Sirsa district, the results of classical and robust unit level SAE were very close, but not in the case of Hisar district. This could be due to the influential observation found in the Hisar data set. More accurate EBLUP wheat yield estimates are obtained when the Huber-type M-estimation method is initialized by the least square regression estimator. [ABSTRACT FROM AUTHOR]

Spatial data contains of observation and region information, can describes spatial patterns such as social phenomenon or poverty. In poverty parameter estimations, the less of sample adequacy to deliver direct estimation is one of the limitation, thus the Small Area Estimation (SAE) developed to handle it. Since, the small area estimation techniques require “borrow strength” across the neighbor areas furthermore SAE was developed by integrating spatial information into the model, named as Spatial SAE. Therefore, the purpose of this paper is to compare the SAE and Spatial SAE model in order to estimate, at sub-district level, mean per capita income of each area using the poverty survey data in Bangka Belitung province at 2017 by Polytechnic of Statistics STIS. The findings of the paper is spatial information don’t influence the parameter estimation in SAE. [ABSTRACT FROM AUTHOR]

Many target variables in official statistics follow a semicontinuous distribution with a mixture of zeros and continuously distributed positive values. Such variables are called zero inflated. When reliable estimates for subpopulations with small sample sizes are required, model-based small-area estimators can be used, which improve the accuracy of the estimates by borrowing information from other subpopulations. In this article, three small-area estimators are investigated. The first estimator is the EBLUP, which can be considered the most common small-area estimator and is based on a linear mixed model that assumes normal distributions. Therefore, the EBLUP is model misspecified in the case of zero-inflated variables. The other two small-area estimators are based on a model that takes zero inflation explicitly into account. Both the Bayesian and the frequentist approach are considered. These small-area estimators are compared with each other and with design-based estimation in a simulation study with zero-inflated target variables. Both a simulation with artificial data and a simulation with real data from the Dutch Household Budget Survey are carried out. It is found that the small-area estimators improve the accuracy compared to the design-based estimator. The amount of improvement strongly depends on the properties of the population and the subpopulations of interest. [ABSTRACT FROM AUTHOR]

If unit-level data are available, small area estimation (SAE) is usually based on models formulated at the unit level, but they are ultimately used to produce estimates at the area level and thus involve area-level inferences. This paper investigates the circumstances under which using an area-level model may be more effective. Linear mixed models (LMMs) fitted using different levels of data are applied in SAE to calculate synthetic estimators and empirical best linear unbiased predictors (EBLUPs). The performance of area-level models is compared with unit-level models when both individual and aggregate data are available. A key factor is whether there are substantial contextual effects. Ignoring these effects in unit-level working models can cause biased estimates of regression parameters. The contextual effects can be automatically accounted for in the area-level models. Using synthetic and EBLUP techniques, small area estimates based on different levels of LMMs are investigated in this paper by means of a simulation study. [ABSTRACT FROM AUTHOR]

Small area estimates based on the widely used area-level model proposed in Fay and Herriot (1979) assume that the area-level direct estimates are spatially uncorrelated. In many cases, however, this is not the case. Extensions of the Fay-Herriot model to allow for spatial correlation have been proposed, but all assume spatial stationarity; i.e., the parameters of the associated regression model for the small area characteristic of interest do not vary spatially. Instead, spatial effects are introduced by imposing a spatial correlation structure on the regression errors. In this paper, we propose an extension to the Fay-Herriot model that accounts for the presence of spatial nonstationarity, i.e., where the parameters of this regression model vary spatially. We refer to the predictor based on this extended model as the nonstationary empirical best linear unbiased predictor (NSEBLUP). We also develop two different estimators for the mean squared error of the NSEBLUP. The first estimator uses approximations similar to those in Opsomer, Claeskens, Ranalli, Kauermann, and Breidt (2008). The second estimator is based on the parametric bootstrapping approach of Gonzalez-Manteiga, Lombardia, Molina, Morales, and Santamaria (2008) and Molina, Salvati, and Pratesi (2009). Results from model-based and design-based simulation studies using spatially nonstationary data indicate that the NSEBLUP compares favorably with alternative area-level predictors that ignore this spatial nonstationarity. In addition, both proposed methods for estimating its mean squared error seem adequate. [ABSTRACT FROM AUTHOR]

Statistical agencies are interested to report precise estimates of linear parameters from small areas. This goal can be achieved by using model-based inference. In this sense, random regression coefficient models provide a flexible way of modelling the relationship between the target and the auxiliary variables. Because of this, empirical best linear unbiased predictor (EBLUP) estimates based on these models are introduced. A closed-formula procedure to estimate the mean-squared error of the EBLUP estimators is also given and empirically studied. Results of several simulation studies are reported as well as an application to the estimation of household normalized net annual incomes in the Spanish Living Conditions Survey. [ABSTRACT FROM AUTHOR]

We show that the maximum likelihood estimators (MLEs) of the fixed effects and within-cluster correlation are consistent in a heteroscedastic nested-error regression (HNER) model with completely unknown within-cluster variances under mild conditions. The result implies that the empirical best linear unbiased prediction (EBLUP) method for small area estimation is valid in such a case. We also show that ignoring the heteroscedasticity can lead to inconsistent estimation of the within-cluster correlation and inferior predictive performance. A jackknife measure of uncertainty for the EBLUP is developed under the HNER model. Simulation studies are carried out to investigate the finite-sample performance of the EBLUP and MLE under the HNER model, with comparisons to those under the nested-error regression model in various situations, as well as that of the jackknife measure of uncertainty. The well-known Iowa crops data is used for illustration. The Canadian Journal of Statistics 40: 588-603; 2012 © 2012 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

A modification of the Fay-Herriot model is introduced to treat situations where small areas are divided in two groups and domain random effects have different variances across the groups. The model is applicable to data having a large subset of domains where direct estimates of the variable of interest cannot be described in the same way as in its complementary subset of domains. This is generally the case when domains are constructed by crossing geographical characteristics with sex. Algorithms and formulas to fit the model, to calculate EBLUPs and to estimate mean squared errors are given. Monte Carlo simulation experiments are presented to illustrate the gain of precision obtained by using the proposed model and to get some practical conclusions. A motivating application to Spanish Labour Force Survey data is also given. [ABSTRACT FROM AUTHOR]

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163-171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad-Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors. [ABSTRACT FROM AUTHOR]