Estimation of An Optimum Spatial Autocorrelation in Linear Mixed Models Containing Spatial Effects

Fay-Herriot model assumes that the random effects between regions (areas) are independent of each other. This allows the regions to be mutually independent so that the estimators obtained are unbiased estimators. In cases where the regions are not mutually independent, it can develop a model in which the assumptions are violated (not fulfilled) or allow the regions to be dependent. The development of this model is known as small area estimation (SAE) with spatial effects. In small area estimation with spatial effects, one of the important parameters is the spatial autocorrelation parameter. In various small area estimation with spatial effects, it is still very rare to generate estimators of the spatial autocorrelation parameter. Most of the parameter values used are known, that is by trying to enter several spatial autocorrelation parameter values to show that the addition of regional aspects can increase the accuracy of the small area estimation. In addition, they have also tried a restricted maximum likelihood approach in estimating the spatial autocorrelation and component variance but they still assume that the sampling variance is known (assigned). Therefore, this research proposes a concentrated log-likelihood function by means of numerical procedure to find an optimum estimate value for spatial autocorrelation coefficient where both a sampling variance and a component variance are unknown. Parameters estimators obtained in the models, fixed and random effects parameters, are proved to be consistent.

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Applying the Spatial EBLUP to Place-Based Policing. Simulation Study and Application to Confidence in Police Work

Applied Spatial Analysis and Policy ◽

10.1007/s12061-020-09333-8 ◽

2020 ◽

Vol 13 (4) ◽

pp. 901-924

Author(s):

David Buil-Gil ◽

Angelo Moretti ◽

Natalie Shlomo ◽

Juanjo Medina

Keyword(s):

Spatial Autocorrelation ◽

Random Effects ◽

Simulation Study ◽

Small Area ◽

Police Work ◽

Best Linear Unbiased Predictor ◽

Spatial Random Effects ◽

Area Estimation ◽

Best Linear Unbiased ◽

Estimation Models

Abstract There is growing need for reliable survey-based small area estimates of crime and confidence in police work to design and evaluate place-based policing strategies. Crime and confidence in policing are geographically aggregated and police resources can be targeted to areas with the most problems. High levels of spatial autocorrelation in these variables allow for using spatial random effects to improve small area estimation models and estimates’ reliability. This article introduces the Spatial Empirical Best Linear Unbiased Predictor (SEBLUP), which borrows strength from neighboring areas, to place-based policing. It assesses the SEBLUP under different scenarios of number of areas and levels of spatial autocorrelation and provides an application to confidence in policing in London. The SEBLUP should be applied for place-based policing strategies when the variable’s spatial autocorrelation is medium/high, and the number of areas is large. Confidence in policing is higher in Central and West London and lower in Eastern neighborhoods.

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Simulation Study of Robust Geographically Weighted Empirical Best Linear Unbiased Predictor on Small Area Estimation

Indonesian Journal of Statistics and Its Applications ◽

10.29244/ijsa.v5i1p50-60 ◽

2021 ◽

Vol 5 (1) ◽

pp. 50-60

Author(s):

Naima Rakhsyanda ◽

Kusman Sadik ◽

Indahwati Indahwati

Keyword(s):

Small Area ◽

Spatial Information ◽

Mean Squared Error ◽

Small Area Estimation ◽

Small Sample ◽

Population Parameter ◽

Spatial Effects ◽

Best Linear Unbiased Predictor ◽

Area Estimation ◽

Best Linear Unbiased

Small area estimation can be used to predict the population parameter with small sample sizes. For some cases, the population units that are close spatially may be more related than units that are further apart. The use of spatial information like geographic coordinates are studied in this research. Outlier contaminations can affect small area estimations. This study was conducted using simulation methods on generated data with six scenarios. The scenarios are the combination of spatial effects (spatial stationary and spatial non-stationary) with outlier contamination (no outlier, symmetric outliers, and non-symmetric outliers). The purpose of this study was to compare the geographically weighted empirical best linear unbiased predictor (GWEBLUP) and robust GWEBLUP (RGWEBLUP) with direct estimator, EBLUP, and REBLUP using simulation data. The performance of the predictors is evaluated using relative root mean squared error (RRMSE). The simulation results showed that geographically weighted predictors have the smallest RRMSE values for scenarios with spatial non-stationary, therefore offer a better prediction. For scenarios with outliers, robust predictors with smaller RRMSE values offer more efficiency than non-robust predictors.

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