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Articles de revues sur le sujet « Latent Models, Small Area Estimation »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 10 mars 2023

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1

Porter, Aaron T., Christopher K. Wikle, and Scott H. Holan. "Small Area Estimation via Multivariate Fay-Herriot Models with Latent Spatial Dependence." Australian & New Zealand Journal of Statistics 57, no. 1 (2015): 15–29. http://dx.doi.org/10.1111/anzs.12101.

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Choi, Jungsoon, and Andrew B. Lawson. "Bayesian spatially dependent variable selection for small area health modeling." Statistical Methods in Medical Research 27, no. 1 (2016): 234–49. http://dx.doi.org/10.1177/0962280215627184.

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Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

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Thomas, Neal. "Assessing Model Sensitivity of the Imputation Methods Used in the National Assessment of Educational Progress." Journal of Educational and Behavioral Statistics 25, no. 4 (2000): 351–71. http://dx.doi.org/10.3102/10769986025004351.

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The National Assessment of Educational Progress (NAEP) uses latent trait item response models to summarize performance of students on assessments of educational proficiency in different subject areas such as mathematics and reading. Because of limited examination time and concerns about student motivation. NAEP employs sparse matrix sampling designs that assign a small number of examination items to each sampled student to measure broad curriculums. As a consequence, each sampled student’s latent trait is not accurately measured, and NAEP uses multiple imputation missing data statistical methods to account for the uncertainty about the latent traits. The sensitivity of these model-based estimation and reporting procedures to statistical and psychometric assumptions is assessed. Estimation of the mean of the latent trait train different subpopulations was very robust to the modeling assumptions. Many of the other currently reported summaries, however; may depend on the modeling assumptions underlying the estimation procedures; these assumptions, motivated primarily by analytic tractability, are unlikely to attain, raising concerns about current reporting practices. The results indicate that more conservative criteria should be considered when forming intervals about estimates, and when assessing significance. A possible expansion of the imputation model is suggested that may improve its performance.

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Marcq, S., and J. Weiss. "Influence of leads widths distribution on turbulent heat transfer between the ocean and the atmosphere." Cryosphere Discussions 5, no. 5 (2011): 2765–97. http://dx.doi.org/10.5194/tcd-5-2765-2011.

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Abstract. Leads are linear-like structures of open water within the sea ice cover that develop as the result of fracturing due to divergence or shear. Through leads, air and water come into contact and directly exchange latent and sensible heat through convective processes driven by the large temperature and moisture differences between them. In the central Arctic, leads only cover 1 to 2% of the ocean during winter, but account for more than 80% of the heat fluxes. Furthermore, narrow leads (several meters) are more than twice as efficient at transmitting turbulent heat than larger ones (several hundreds of meters). We show that lead widths are power law distributed, P(X)~X−a with a>1, down to very small spatial scales (20 m or below). This implies that the open water fraction is by far dominated by very small leads. Using two classical formulations, which provide first order turbulence closure for the fetch-dependence of heat fluxes, we find that the mean heat fluxes (sensible and latent) over open water are up to 55 % larger when considering the lead width distribution obtained from a SPOT satellite image of the ice cover, compared to the situation where the open water fraction constitutes one unique large lead and the rest of the area is covered by ice, as it is usually considered in climate models at the grid scale. This difference may be even larger if we assume that the power law scaling of lead widths extents down to smaller (~1 m) scales. Such estimations may be a first step towards a subgrid scale parameterization of the spatial distribution of open water for heat fluxes calculations in ocean/sea ice coupled models.

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Marcq, S., and J. Weiss. "Influence of sea ice lead-width distribution on turbulent heat transfer between the ocean and the atmosphere." Cryosphere 6, no. 1 (2012): 143–56. http://dx.doi.org/10.5194/tc-6-143-2012.

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Abstract. Leads are linear-like structures of open water within the sea ice cover that develop as the result of fracturing due to divergence or shear. Through leads, air and water come into contact and directly exchange latent and sensible heat through convective processes driven by the large temperature and moisture differences between them. In the central Arctic, leads only cover 1 to 2% of the ocean during winter, but account for more than 70% of the upward heat fluxes. Furthermore, narrow leads (several meters) are more than twice as efficient at transmitting turbulent heat than larger ones (several hundreds of meters). We show that lead widths are power law distributed, P(X)~X−a with a>1, down to very small spatial scales (20 m or below). This implies that the open water fraction is by far dominated by very small leads. Using two classical formulations, which provide first order turbulence closure for the fetch-dependence of heat fluxes, we find that the mean heat fluxes (sensible and latent) over open water are up to 55% larger when considering the lead-width distribution obtained from a SPOT satellite image of the ice cover, compared to the situation where the open water fraction constitutes one unique large lead and the rest of the area is covered by ice, as it is usually considered in climate models at the grid scale. This difference may be even larger if we assume that the power law scaling of lead widths extends down to smaller (~1 m) scales. Such estimations may be a first step towards a subgrid scale parameterization of the spatial distribution of open water for heat fluxes calculations in ocean/sea ice coupled models.

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Nassar, Ayman, Alfonso Torres-Rua, Lawrence Hipps, et al. "Using Remote Sensing to Estimate Scales of Spatial Heterogeneity to Analyze Evapotranspiration Modeling in a Natural Ecosystem." Remote Sensing 14, no. 2 (2022): 372. http://dx.doi.org/10.3390/rs14020372.

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Understanding the spatial variability in highly heterogeneous natural environments such as savannas and river corridors is an important issue in characterizing and modeling energy fluxes, particularly for evapotranspiration (ET) estimates. Currently, remote-sensing-based surface energy balance (SEB) models are applied widely and routinely in agricultural settings to obtain ET information on an operational basis for use in water resources management. However, the application of these models in natural environments is challenging due to spatial heterogeneity in vegetation cover and complexity in the number of vegetation species existing within a biome. In this research effort, small unmanned aerial systems (sUAS) data were used to study the influence of land surface spatial heterogeneity on the modeling of ET using the Two-Source Energy Balance (TSEB) model. The study area is the San Rafael River corridor in Utah, which is a part of the Upper Colorado River Basin that is characterized by arid conditions and variations in soil moisture status and the type and height of vegetation. First, a spatial variability analysis was performed using a discrete wavelet transform (DWT) to identify a representative spatial resolution/model grid size for adequately solving energy balance components to derive ET. The results indicated a maximum wavelet energy between 6.4 m and 12.8 m for the river corridor area, while the non-river corridor area, which is characterized by different surface types and random vegetation, does not show a peak value. Next, to evaluate the effect of spatial resolution on latent heat flux (LE) estimation using the TSEB model, spatial scales of 6 m and 15 m instead of 6.4 m and 12.8 m, respectively, were used to simplify the derivation of model inputs. The results indicated small differences in the LE values between 6 m and 15 m resolutions, with a slight decrease in detail at 15 m due to losses in spatial variability. Lastly, the instantaneous (hourly) LE was extrapolated/upscaled to daily ET values using the incoming solar radiation (Rs) method. The results indicated that willow and cottonwood have the highest ET rates, followed by grass/shrubs and treated tamarisk. Although most of the treated tamarisk vegetation is in dead/dry condition, the green vegetation growing underneath resulted in a magnitude value of ET.

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Babel, W., S. Huneke, and T. Foken. "A framework to utilize turbulent flux measurements for mesoscale models and remote sensing applications." Hydrology and Earth System Sciences Discussions 8, no. 3 (2011): 5165–225. http://dx.doi.org/10.5194/hessd-8-5165-2011.

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Abstract. Meteorologically measured fluxes of energy and matter between the surface and the atmosphere originate from a source area of certain extent, located in the upwind sector of the device. The spatial representativeness of such measurements is strongly influenced by the heterogeneity of the landscape. The footprint concept is capable of linking observed data with spatial heterogeneity. This study aims at upscaling eddy covariance derived fluxes to a grid size of 1 km edge length, which is typical for mesoscale models or low resolution remote sensing data. Here an upscaling strategy is presented, utilizing footprint modelling and SVAT modelling as well as observations from a target land-use area. The general idea of this scheme is to model fluxes from adjacent land-use types and combine them with the measured flux data to yield a grid representative flux according to the land-use distribution within the grid cell. The performance of the upscaling routine is evaluated with real datasets, which are considered to be land-use specific fluxes in a grid cell. The measurements above rye and maize fields stem from the LITFASS experiment 2003 in Lindenberg, Germany and the respective modelled timeseries were derived by the SVAT model SEWAB. Contributions from each land-use type to the observations are estimated using a forward lagrangian stochastic model. A representation error is defined as the error in flux estimates made when accepting the measurements unchanged as grid representative flux and ignoring flux contributions from other land-use types within the respective grid cell. Results show that this representation error can be reduced up to 56 % when applying the spatial integration. This shows the potential for further application of this strategy, although the absolute differences between flux observations from rye and maize were so small, that the spatial integration would be rejected in a real situation. Corresponding thresholds for this decision have been estimated as a minimum mean absolute deviation in modelled timeseries of the different land-use types with 35 W m−2 for the sensible heat flux and 50 W m−2 for the latent heat flux. Finally, a quality lagging scheme to classify the data with respect to representativeness for a given grid cell is proposed, based on an overall flux error estimate. This enables the data user to infer the uncertainty of mesoscale models and remote sensing products with respect to ground observations. Major uncertainty sources remaining are the lack of an adequate method for energy balance closure correction as well as model structure and parameter estimation, when applying the model for surfaces without flux measurements.

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Klees, R., E. A. Zapreeva, H. C. Winsemius, and H. H. G. Savenije. "The bias in GRACE estimates of continental water storage variations." Hydrology and Earth System Sciences Discussions 3, no. 6 (2006): 3557–94. http://dx.doi.org/10.5194/hessd-3-3557-2006.

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Abstract. The estimation of terrestrial water storage variations at river basin scale is among the best documented applications of the GRACE (Gravity and Climate Experiment) satellite gravity mission. In particular, it is expected that GRACE closes the water balance at river basin scale and allows the verification, improvement and modeling of the related hydrological processes by combining GRACE amplitude estimates with hydrological models' output and in-situ data. When computing monthly mean storage variations from GRACE gravity field models, spatial filtering is mandatory to reduce GRACE errors, but at the same time yields biased amplitude estimates. The objective of this paper is three-fold. Firstly, we want to compute and analyze amplitude and time behaviour of the bias in GRACE estimates of monthly mean water storage variations for several target areas in Southern Africa. In particular, we want to know the relation between bias and the choice of the filter correlation length, the size of the target area, and the amplitude of mass variations inside and outside the target area. Secondly, we want to know to what extent the bias can be corrected for using a priori information about mass variations. Thirdly, we want to quantify errors in the estimated bias due to uncertainties in the a priori information about mass variations that are used to compute the bias. The target areas are located in Southern Africa around the Zambezi river basin. The latest release of monthly GRACE gravity field models have been used for the period from January 2003 until March 2006. An accurate and properly calibrated regional hydrological model has been developed for this area and its surroundings and provides the necessary a priori information about mass variations inside and outside the target areas. The main conclusion of the study is that spatial smoothing significantly biases GRACE estimates of the amplitude of annual and monthly mean water storage variations. For most of the practical applications, the bias will be positive, which implies that GRACE underestimates the amplitudes. The bias is mainly determined by the filter correlation length; in the case of 1000 km smoothing, which is shown to be an appropriate choice for the target areas, the annual bias attains values up to 50% of the annual storage; the monthly bias is even larger with a maximum value of 75% of the monthly storage. A priori information about mass variations can provide reasonably accurate estimates of the bias, which significantly improves the quality of GRACE water storage amplitudes. For the target areas in Southern Africa, we show that after bias correction, GRACE annual amplitudes differ between 0 and 30 mm from the output of a regional hydrological model, which is between 0% and 25% of the storage. Annual phase shifts are small, not exceeding 0.25 months, i.e. 7.5 deg. Our analysis suggests that bias correction of GRACE water storage amplitudes is indispensable if GRACE is used to calibrate hydrological models.

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Klees, R., E. A. Zapreeva, H. C. Winsemius, and H. H. G. Savenije. "The bias in GRACE estimates of continental water storage variations." Hydrology and Earth System Sciences 11, no. 4 (2007): 1227–41. http://dx.doi.org/10.5194/hess-11-1227-2007.

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Abstract. The estimation of terrestrial water storage variations at river basin scale is among the best documented applications of the GRACE (Gravity and Climate Experiment) satellite gravity mission. In particular, it is expected that GRACE closes the water balance at river basin scale and allows the verification, improvement and modeling of the related hydrological processes by combining GRACE amplitude estimates with hydrological models' output and in-situ data. When computing monthly mean storage variations from GRACE gravity field models, spatial filtering is mandatory to reduce GRACE errors, but at the same time yields biased amplitude estimates. The objective of this paper is three-fold. Firstly, we want to compute and analyze amplitude and time behaviour of the bias in GRACE estimates of monthly mean water storage variations for several target areas in Southern Africa. In particular, we want to know the relation between bias and the choice of the filter correlation length, the size of the target area, and the amplitude of mass variations inside and outside the target area. Secondly, we want to know to what extent the bias can be corrected for using a priori information about mass variations. Thirdly, we want to quantify errors in the estimated bias due to uncertainties in the a priori information about mass variations that are used to compute the bias. The target areas are located in Southern Africa around the Zambezi river basin. The latest release of monthly GRACE gravity field models have been used for the period from January 2003 until March 2006. An accurate and properly calibrated regional hydrological model has been developed for this area and its surroundings and provides the necessary a priori information about mass variations inside and outside the target areas. The main conclusion of the study is that spatial smoothing significantly biases GRACE estimates of the amplitude of annual and monthly mean water storage variations and that bias correction using existing hydrological models significantly improves the quality of GRACE estimates. For most of the practical applications, the bias will be positive, which implies that GRACE underestimates the amplitudes. The bias is mainly determined by the filter correlation length; in the case of 1000 km smoothing, which is shown to be an appropriate choice for the target areas, the annual bias attains values up to 50% of the annual storage; the monthly bias is even larger with a maximum value of 75% of the monthly storage. A priori information about mass variations can provide reasonably accurate estimates of the bias, which significantly improves the quality of GRACE water storage amplitudes. For the target areas in Southern Africa, we show that after bias correction, GRACE annual amplitudes differ between 0 and 30 mm from the output of a regional hydrological model, which is between 0% and 25% of the storage. Annual phase shifts are small, not exceeding 0.25 months, i.e. 7.5 deg. It is shown that after bias correction, the fit between GRACE and a hydrological model is overoptimistic, if the same hydrological model is used to estimate the bias and to compare with GRACE. If another hydrological model is used to compute the bias, the fit is less, although the improvement is still very significant compared with uncorrected GRACE estimates of water storage variations. Therefore, the proposed approach for bias correction works for the target areas subject to this study. It may also be an option for other target areas provided that some reasonable a priori information about water storage variations are available.

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Kubokawa, Tatsuya. "Linear Mixed Models and Small Area Estimation." Japanese journal of applied statistics 35, no. 3 (2006): 139–61. http://dx.doi.org/10.5023/jappstat.35.139.

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Dagne, Getachew A. "Bayesian transformed models for small area estimation." Test 10, no. 2 (2001): 375–91. http://dx.doi.org/10.1007/bf02595703.

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Benedetti, Roberto, Monica Pratesi, and Nicola Salvati. "Local stationarity in small area estimation models." Statistical Methods & Applications 22, no. 1 (2012): 81–95. http://dx.doi.org/10.1007/s10260-012-0208-1.

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Chambers, Ray, and Nikos Tzavidis. "M-quantile models for small area estimation." Biometrika 93, no. 2 (2006): 255–68. http://dx.doi.org/10.1093/biomet/93.2.255.

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Ghosh, Malay, Kannan Natarajan, T. W. F. Stroud, and Bradley P. Carlin. "Generalized Linear Models for Small-Area Estimation." Journal of the American Statistical Association 93, no. 441 (1998): 273–82. http://dx.doi.org/10.1080/01621459.1998.10474108.

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Ferraz, V. R. S., and F. A. S. Moura. "Small area estimation using skew normal models." Computational Statistics & Data Analysis 56, no. 10 (2012): 2864–74. http://dx.doi.org/10.1016/j.csda.2011.07.005.

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Moretti, Angelo, Natalie Shlomo, and Joseph W. Sakshaug. "Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators." International Statistical Review 88, no. 1 (2020): 1–28. http://dx.doi.org/10.1111/insr.12333.

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Zhang, Junni L., and John Bryant. "Fully Bayesian Benchmarking of Small Area Estimation Models." Journal of Official Statistics 36, no. 1 (2020): 197–223. http://dx.doi.org/10.2478/jos-2020-0010.

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AbstractEstimates for small areas defined by social, demographic, and geographic variables are increasingly important for official statistics. To overcome problems of small sample sizes, statisticians usually derive model-based estimates. When aggregated, however, the model- based estimates typically do not agree with aggregate estimates (benchmarks) obtained through more direct methods. This lack of agreement between estimates can be problematic for users of small area estimates. Benchmarking methods have been widely used to enforce agreement. Fully Bayesian benchmarking methods, in the sense of yielding full posterior distributions after benchmarking, can provide coherent measures of uncertainty for all quantities of interest, but research on fully Bayesian benchmarking methods is limited. We present a flexible fully Bayesian approach to benchmarking that allows for a wide range of models and benchmarks. We revise the likelihood by multiplying it by a probability distribution that measures agreement with the benchmarks. We outline Markov chain Monte Carlo methods to generate samples from benchmarked posterior distributions. We present two simulations, and an application to English and Welsh life expectancies.

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Hobza, Tomáš, and Domingo Morales. "Small area estimation under random regression coefficient models." Journal of Statistical Computation and Simulation 83, no. 11 (2012): 2160–77. http://dx.doi.org/10.1080/00949655.2012.684094.

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Logan, John R., Cici Bauer, Jun Ke, Hongwei Xu, and Fan Li. "Models for Small Area Estimation for Census Tracts." Geographical Analysis 52, no. 3 (2019): 325–50. http://dx.doi.org/10.1111/gean.12215.

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Benavent, Roberto, and Domingo Morales. "Multivariate Fay–Herriot models for small area estimation." Computational Statistics & Data Analysis 94 (February 2016): 372–90. http://dx.doi.org/10.1016/j.csda.2015.07.013.

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Sugasawa, Shonosuke, and Tatsuya Kubokawa. "Small area estimation with mixed models: a review." Japanese Journal of Statistics and Data Science 3, no. 2 (2020): 693–720. http://dx.doi.org/10.1007/s42081-020-00076-x.

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Fabrizi, Enrico, and Carlo Trivisano. "Robust linear mixed models for Small Area Estimation." Journal of Statistical Planning and Inference 140, no. 2 (2010): 433–43. http://dx.doi.org/10.1016/j.jspi.2009.07.022.

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von Rosen, Tatjana, and Dietrich von Rosen. "Small area estimation using reduced rank regression models." Communications in Statistics - Theory and Methods 49, no. 13 (2019): 3286–97. http://dx.doi.org/10.1080/03610926.2019.1586946.

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Berg, Emily. "Construction of Databases for Small Area Estimation." Journal of Official Statistics 38, no. 3 (2022): 673–708. http://dx.doi.org/10.2478/jos-2022-0031.

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Abstract The demand for small area estimates can conflict with the objective of producing a multi-purpose data set. We use donor imputation to construct a database that supports small area estimation. Appropriately weighted sums of observed and imputed values produce model-based small area estimates. We develop imputation procedures for both unit-level and area-level models. For area-level models, we restrict to linear models. We assume a single vector of covariates is used for a possibly multivariate response. Each record in the imputed data set has complete data, an estimation weight, and a set of replicate weights for mean square error (MSE) estimation. We compare imputation procedures based on area-level models to those based on unit-level models through simulation. We apply the methods to the Iowa Seat-Belt Use Survey, a survey designed to produce state-level estimates of the proportions of vehicle occupants who wear a seat-belt. We develop a bivariate unit-level model for prediction of county-level proportions of belted drivers and total occupants. We impute values for the proportions of belted drivers and vehicle occupants onto the full population of road segments in the sampling frame. The resulting imputed data set returns approximations for the county-level predictors based on the bivariate model.

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Choi, Jungsoon, Andrew B. Lawson, Bo Cai, and Md Monir Hossain. "Evaluation of Bayesian spatiotemporal latent models in small area health data." Environmetrics 22, no. 8 (2011): 1008–22. http://dx.doi.org/10.1002/env.1127.

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Torkashvand, Elaheh, Mohammad Jafari Jozani, and Mahmoud Torabi. "Clustering in small area estimation with area level linear mixed models." Journal of the Royal Statistical Society: Series A (Statistics in Society) 180, no. 4 (2017): 1253–79. http://dx.doi.org/10.1111/rssa.12308.

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Esteban, María Dolores, María José Lombardía, Esther López-Vizcaíno, Domingo Morales, and Agustín Pérez. "Small area estimation of proportions under area-level compositional mixed models." TEST 29, no. 3 (2019): 793–818. http://dx.doi.org/10.1007/s11749-019-00688-w.

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Esteban, M. D., D. Morales, A. Pérez, and L. Santamaría. "Small area estimation of poverty proportions under area-level time models." Computational Statistics & Data Analysis 56, no. 10 (2012): 2840–55. http://dx.doi.org/10.1016/j.csda.2011.10.015.

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Hoshino, Tadao. "SEMIPARAMETRIC ESTIMATION OF CENSORED SPATIAL AUTOREGRESSIVE MODELS." Econometric Theory 36, no. 1 (2019): 48–85. http://dx.doi.org/10.1017/s0266466618000488.

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This study considers the estimation of spatial autoregressive models with censored dependent variables, where the spatial autocorrelation exists within the uncensored latent dependent variables. The estimator proposed in this paper is semiparametric, in the sense that the error distribution is not parametrically specified and can be heteroskedastic. Under a median restriction, we show that the proposed estimator is consistent and asymptotically normally distributed. As an empirical illustration, we investigate the determinants of the risk of assault and other violent crimes including injury in the Tokyo metropolitan area.

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Young, Linda J., and Lu Chen. "Using Small Area Estimation to Produce Official Statistics." Stats 5, no. 3 (2022): 881–97. http://dx.doi.org/10.3390/stats5030051.

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The USDA National Agricultural Statistics Service (NASS) and other federal statistical agencies have used probability-based surveys as the foundation for official statistics for over half a century. Non-survey data that can be used to improve the accuracy and precision of estimates such as administrative, remotely sensed, and retail data have become increasingly available. Both frequentist and Bayesian models are used to combine survey and non-survey data in a principled manner. NASS has recently adopted Bayesian subarea models for three of its national programs: farm labor, crop county estimates, and cash rent county estimates. Each program provides valuable estimates at multiple scales of geography. For each program, technical challenges had to be met and a strenuous review completed before models could be adopted as the foundation for official statistics. Moving models out of the research phase into production required major changes in the production process and a cultural shift. With the implemented models, NASS now has measures of uncertainty, transparency, and reproducibility of its official statistics.

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You, Yong, and J. N. K. Rao. "Small area estimation using unmatched sampling and linking models." Canadian Journal of Statistics 30, no. 1 (2002): 3–15. http://dx.doi.org/10.2307/3315862.

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Rai, Anil, N. K. Gupta, and Randhir Singh. "Small area estimation of crop production using spatial models." Model Assisted Statistics and Applications 2, no. 2 (2007): 89–98. http://dx.doi.org/10.3233/mas-2007-2204.

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Pusponegoro, Novi Hidayat, Anik Djuraidah, Anwar Fitrianto, and I. Made Sumertajaya. "Geo-additive Models in Small Area Estimation of Poverty." Journal of Data Science and Its Applications 2, no. 1 (2019): 59–67. http://dx.doi.org/10.21108/jdsa.2019.2.15.

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Spatial data contains of observation and region information, it can describe spatial patterns such as disease distribution, reproductive outcome and poverty. The main flaw in direct estimation especially in poverty research is the sample adequacy fulfilment otherwise it will produce large estimate parameter variant. The Small Area Estimation (SAE) developed to handle that flaw. Since, the small area estimation techniques require “borrow strength” across the neighbor areas thus SAE was developed by integrating spatial information into the model, named as Spatial SAE. SAE and spatial SAE model require the fulfilment of covariate linearity assumption as well as the normality of the response distribution that is sometimes violated, and the geo-additive model offers to handle that violation using the smoothing function. Therefore, the purpose of this paper is to compare the SAE, Spatial SAE and Geo-additive model in order to estimate at sub-district level mean of 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 are the Geo-additive is the best fit model based on AIC, and spatial information don't influence the estimation in SAE and spatial SAE model since they have the similar estimation performance.

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Moura, F. AS, and H. S. Migon. "Bayesian spatial models for small area estimation of proportions." Statistical Modelling: An International Journal 2, no. 3 (2002): 183–201. http://dx.doi.org/10.1191/1471082x02st032oa.

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Maiti, Tapabrata. "Robust generalized linear mixed models for small area estimation." Journal of Statistical Planning and Inference 98, no. 1-2 (2001): 225–38. http://dx.doi.org/10.1016/s0378-3758(00)00302-5.

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Sugasawa, Shonosuke, Tatsuya Kubokawa, and J. N. K. Rao. "Small area estimation via unmatched sampling and linking models." TEST 27, no. 2 (2017): 407–27. http://dx.doi.org/10.1007/s11749-017-0551-5.

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Sinha, Sanjoy K. "Robust small area estimation in generalized linear mixed models." METRON 77, no. 3 (2019): 201–25. http://dx.doi.org/10.1007/s40300-019-00161-6.

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Marhuenda, Yolanda, Isabel Molina, and Domingo Morales. "Small area estimation with spatio-temporal Fay–Herriot models." Computational Statistics & Data Analysis 58 (February 2013): 308–25. http://dx.doi.org/10.1016/j.csda.2012.09.002.

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Rao, Jon N. K., Sanjoy K. Sinha, and Laura Dumitrescu. "Robust small area estimation under semi-parametric mixed models." Canadian Journal of Statistics 42, no. 1 (2013): 126–41. http://dx.doi.org/10.1002/cjs.11199.

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Torabi, Mahmoud. "Spatial generalized linear mixed models in small area estimation." Canadian Journal of Statistics 47, no. 3 (2019): 426–37. http://dx.doi.org/10.1002/cjs.11502.

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Li, Huapeng, Yukun Liu, and Riquan Zhang. "Small area estimation under transformed nested-error regression models." Statistical Papers 60, no. 4 (2017): 1397–418. http://dx.doi.org/10.1007/s00362-017-0879-7.

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Jiang, Jiming, and J. Sunil Rao. "Robust Small Area Estimation: An Overview." Annual Review of Statistics and Its Application 7, no. 1 (2020): 337–60. http://dx.doi.org/10.1146/annurev-statistics-031219-041212.

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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 SAE methods 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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Sugasawa, Shonosuke, and Tatsuya Kubokawa. "Correction to: Small area estimation with mixed models: a review." Japanese Journal of Statistics and Data Science 4, no. 1 (2021): 477. http://dx.doi.org/10.1007/s42081-021-00108-0.

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Jeong, Seok-Oh, and Key-Il Shin. "Semiparametric and Nonparametric Mixed Effects Models for Small Area Estimation." Korean Journal of Applied Statistics 26, no. 1 (2013): 71–79. http://dx.doi.org/10.5351/kjas.2013.26.1.071.

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Morales, Domingo, and Laureano Santamaría. "Small area estimation under unit-level temporal linear mixed models." Journal of Statistical Computation and Simulation 89, no. 9 (2019): 1592–620. http://dx.doi.org/10.1080/00949655.2019.1590578.

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Datta, Gauri Sankar, and Malay Ghosh. "Bayesian Prediction in Linear Models: Applications to Small Area Estimation." Annals of Statistics 19, no. 4 (1991): 1748–70. http://dx.doi.org/10.1214/aos/1176348369.

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Torabi, Mahmoud, and Farhad Shokoohi. "Non-parametric generalized linear mixed models in small area estimation." Canadian Journal of Statistics 43, no. 1 (2015): 82–96. http://dx.doi.org/10.1002/cjs.11236.

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González-Manteiga, W., MJ Lombarda, I. Molina, D. Morales, and L. Santamaría. "Small area estimation under Fay–Herriot models with non-parametric estimation of heteroscedasticity." Statistical Modelling: An International Journal 10, no. 2 (2010): 215–39. http://dx.doi.org/10.1177/1471082x0801000206.

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Pereira, Luis Nobre, and Pedro Simões Coelho. "An Applied Comparison of Area-Level Linear Mixed Models in Small Area Estimation." Communications in Statistics - Simulation and Computation 42, no. 3 (2013): 671–85. http://dx.doi.org/10.1080/03610918.2011.654029.

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Souza, Debora F., and Fernando A. S. Moura. "Multivariate Beta Regression with Application in Small Area Estimation." Journal of Official Statistics 32, no. 3 (2016): 747–68. http://dx.doi.org/10.1515/jos-2016-0038.

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Abstract Multivariate beta regression models for jointly modelling two or more variables whose values belong in the (0,1) interval, such as indexes, rates or proportions, are proposed for making small area predictions. The multivariate model can help the estimation process by borrowing strength between units and obtaining more precise estimates, especially for small samples. Each response variable is assumed to have a beta distribution so the models could accommodate multivariate asymmetric data. Copula functions are used to construct the joint distribution of the dependent variables; all the marginal distributions are fixed as beta. A hierarchical beta regression model is additionally proposed with correlated random effects. We present an illustration of the proposed approach by estimating two indexes of educational attainment at school level in a Brazilian state. Our predictions are compared with separate univariate beta regressions. The inference process was conducted using a full Bayesian approach.

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