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

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.

scholarly journals Simple House Needs in Jember with Robust Small Area Estimation

2017 ◽  
Vol 18 (1) ◽  
pp. 1
Author(s):  
Frida Murtinasari ◽  
Alfian Futuhul Hadi ◽  
Dian Anggraeni
Keyword(s):  
Small Area ◽  
Robust Regression ◽  
Small Sample Size ◽  
Small Area Estimation ◽  
Small Sample ◽  
Estimation Methods ◽  
Linear Unbiased Prediction ◽  
Area Estimation ◽  
Best Linear Unbiased ◽  
M Estimation

SAE (Small Area Estimation) is often used by researchers, especially statisticians to estimate parameters of a subpopulation which has a small sample size. Empirical Best Linear Unbiased Prediction (EBLUP) is one of the indirect estimation methods in Small Area Estimation. The presence of outliers in the data can not guarantee that these methods yield precise predictions . Robust regression is one approach that is used in the model Small Area Estimation. Robust approach in estimating such a small area known as the Robust Small Area Estimation. Robust Small Area Estimation divided into several approaches. It calls Maximum Likelihood and M- Estimation. From the result, Robust Small Area Estimation with M-Estimation has the smallest RMSE than others. The value is 1473.7 (with outliers) and 1279.6 (without outlier). In addition the research also indicated that REBLUP with M-Estimation more robust to outliers. It causes the RMSE value with EBLUP has five times to be large with only one outlier are included in the data analysis. As for the REBLUP method is relatively more stable RMSE results.

scholarly journals PENDUGAAN AREA KECIL UNTUK ANGKA PARTISIPASI KASAR PENDIDIKAN DASAR DAN MENENGAH TINGKAT KABUPATEN/KOTA DI PROVINSI JAWA TENGAH TAHUN 2018

2021 ◽  
Vol 2020 (1) ◽  
pp. 651-661
Author(s):  
Gusti Firmando ◽  
Azka Ubaidillah
Keyword(s):  
Small Area ◽  
Small Area Estimation ◽  
Best Linear Unbiased Predictor ◽  
Area Estimation ◽  
Best Linear Unbiased

Pada Maret tahun 2018, Angka Partisipasi Kasar (APK) di Indonesia untuk pendidikan dasar dan menengah adalah sebesar: APK SD/sederajat 108,61%, APK SMP/sederajat 91,52%, sedangkan APK SMA/sederajat 80,68%. Capaian tersebut masih jauh dari target Rencana Pembangunan Jangka Menengah Nasional (RPJMN) 2014-2019. Salah satu provinsi yang memiliki APK pendidikan dasar dan menengah di bawah target RPJMN adalah Provinsi Jawa Tengah. Upaya yang dapat dilakukan untuk mewujudkan target tersebut adalah dengan mengetahui capaian APK pendidikan dasar dan menengah di level kabupaten/kota berdasarkan hasil Susenas September sehingga kontrol dapat dilakukan dua kali dalam setahun. Namun, langkah ini akan memerlukan penambahan jumlah sampel yang menyebabkan diperlukannya waktu, biaya, tenaga dan pemikiran yang lebih besar. Untuk mengatasi hal tersebut, Small Area Estimation (SAE) dapat digunakan untuk menghasilkan presisi yang memadai tanpa melakukan penambahan jumlah sampel. SAE merupakan metode pendugaan parameter-parameter subpopulasi yang memiliki ukuran sampel kecil. Metode SAE yang banyak digunakan adalah Empirical Best Linear Unbiased Predictor (EBLUP). Namun, model ini belum memasukkan pengaruh spasial ke dalam model. Model Fay-Herriot yang memerhatikan efek spasial dikenal dengan Spatial Empirical Best Linear Unbiased Predictor (SEBLUP). Hasil penelitian menunjukkan bahwa metode EBLUP lebih baik dalam mengestimasi APK SD/sederajat dan APK SMA/sederajat, dan metode SEBLUP lebih baik dalam mengestimasi APK SMP/sederajat.

scholarly journals Small area estimation of socioeconomic indicators for sampled and unsampled domains

2021 ◽  
Author(s):  
Jan Pablo Burgard ◽  
Domingo Morales ◽  
Anna-Lena Wölwer
Keyword(s):  
Small Area ◽  
Large Scale ◽  
Mean Squared Error ◽  
Small Area Estimation ◽  
Small Sample ◽  
Median Income ◽  
Socioeconomic Indicators ◽  
Latino Americans ◽  
Area Estimation ◽  
The Impact

AbstractSocioeconomic indicators play a crucial role in monitoring political actions over time and across regions. Income-based indicators such as the median income of sub-populations can provide information on the impact of measures, e.g., on poverty reduction. Regional information is usually published on an aggregated level. Due to small sample sizes, these regional aggregates are often associated with large standard errors or are missing if the region is unsampled or the estimate is simply not published. For example, if the median income of Hispanic or Latino Americans from the American Community Survey is of interest, some county-year combinations are not available. Therefore, a comparison of different counties or time-points is partly not possible. We propose a new predictor based on small area estimation techniques for aggregated data and bivariate modeling. This predictor provides empirical best predictions for the partially unavailable county-year combinations. We provide an analytical approximation to the mean squared error. The theoretical findings are backed up by a large-scale simulation study. Finally, we return to the problem of estimating the county-year estimates for the median income of Hispanic or Latino Americans and externally validate the estimates.

ESTIMASI ANGKA PARTISIPASI KASAR PERGURUAN TINGGI PROVINSI PAPUA MELALUI SMALL AREA ESTIMATION

2020 ◽  
Vol 2019 (1) ◽  
pp. 104-109
Author(s):  
Budi Subandriyo
Keyword(s):  
Sustainable Development ◽  
Small Area ◽  
Sustainable Development Goals ◽  
Small Area Estimation ◽  
Auxiliary Variable ◽  
Best Linear Unbiased Predictor ◽  
Area Estimation ◽  
Direct Estimation ◽  
Development Goals ◽  
Best Linear Unbiased

Angka Partisipasi Kasar (APK) m0erupakan salah satu indikator statistik yang digunakan untuk melihat besarnya tingkat partisipasi pendidikan pada suatu wilayah. Besar atau kecilnya nilai APK perguruan tinggi menunjukkan seberapa mudah penduduk untuk mengakses Pendidikan di perguruan tinggi. Hal ini sesuai dengan tujuan pembangunan berkelanjutan (Sustainable Development Goals) yang memiliki program untuk terus meningkatkan kesempatan belajar, salah satunya pendidikan di perguruan tinggi. Oleh karena itu, diperlukan upaya peningkatan akses pendidikan di universitas dan perguruan tinggi melalui penyediaan data APK-PT yang akurat. Apabila dilihat berdasarkan daerah tingkat provinsi, Provinsi Papua merupakan provinsi dengan APK-PT dua terbawah di antara provinsi lainnya yaitu sebesar 19,03 persen. Akan tetapi, ketersediaan data APK-PT hingga tingkar kabupaten atau kota masih belum tersedia karena kurangnya ukuran sampel. Salah satu upaya untuk mengoptimalkan sampel yang tersedia dan menghasil estimasi APK-PT di tingkat kabupaten/kota yaitu dengan menggunakan metode Small Area Estimation (SAE) berbasis area level. Pada penelitian ini digunakan data Survei Sosial Ekonomi Nasional (SUSENAS) 2018 untuk memperoleh estimasi langsung (direct estimation) APK-PT dan Potensi Desa (PODES) 2018 di Provinsi Papua sebagai variabel penyerta (auxiliary variable) dalam pemodelan SAE. Metode SAE yang digunakan adalah Empirical Best Linear Unbiased Predictor – Fay Herriot (EBLUP-FH) dan EBLUP benchmarking seperti EBLUP Difference Benchmarking (EBLUP-DB), EBLUP You-Rao Benchmarking (EBLUP-YR), dan EBLUP Augmented Bencharking (EBLUP-AB). Berdasarkan hasil penelitian disimpulkan bahwa penggunaan estimasi SAE yang cocok pada data APK-PT di Provinsi Papua adalah model EBLUP Augmented Benchmarking dengan nilai rata-rata MSE terendah yaitu sebesar 22,06 persen.

scholarly journals ESTIMASI RATA-RATA LAMA SEKOLAH TINGKAT KECAMATAN DI KABUPATEN PADANG PARIAMAN DENGAN METODE EMPIRICAL BEST LINEAR UNBIASED PREDICTOR

2020 ◽  
Vol 2019 (1) ◽  
pp. 110-116
Author(s):  
Rita Diana ◽  
Rory Rory
Keyword(s):  
Maximum Likelihood ◽  
Small Area ◽  
Small Area Estimation ◽  
Restricted Maximum Likelihood ◽  
Best Linear Unbiased Predictor ◽  
Area Estimation ◽  
Best Linear Unbiased

Rata-rata lama sekolah penduduk umur 25 tahun ke atas merupakan salah satu indikator yang menggambarkan tingkat pendidikan penduduk secara keseluruhan. Dari 19 kabupaten/kota di Sumatera Barat, Kabupaten Padang Pariaman memiliki rata-rata lama sekolah terendah kedua setelah Kabupaten Kepulauan Mentawai. Penanganan rendahnya rata-rata lama sekolah membutuhkan tersedianya data rata-rata lama sekolah yang up to date dan menjangkau level wilayah yang kecil seperti kecamatan dan desa/nagari, agar kebijakan yang diambil pemerintah bisa tepat sasaran. Ketersediaan data tersebut belum mampu diakomodir oleh Badan Pusat Statistik (BPS), karena survei yang dilakukan oleh BPS dirancang untuk pendugaan data area besar, yaitu provinsi dan kabupaten. Salah satu solusi untuk masalah tersebut adalah dengan menggunakan metode estimasi tidak langsung, yaitu Small Area Estimation (SAE). Salah satu estimasi parameter secara tidak langsung berbasiskan model SAE adalah Empirical Best Linear Unbiased Predictor (EBLUP). Tujuan penelitian ini adalah melakukan estimasi rata-rata lama sekolah tingkat kecamatan di Kabupaten Padang Pariaman menggunakan metode EBLUP dengan prosedur maximum likelihood (ML) dan prosedur restricted maximum likelihood (REML). Variabel penyerta yang digunakan dalam penelitian ini yang diduga berpengaruh terhadap variabel respon adalah rasio jumlah SLTA/sederajat per 10.000 penduduk, rata-rata jarak terhadap SLTA/sederajat dan persentase keluarga pertanian. Hasil penelitian menunjukkan SAE metode EBLUP dengan prosedur REML menghasilkan nilai estimasi rata-rata lama sekolah tingkat kecamatan di kabupaten Padang Pariaman memiliki akurasi yang lebih baik dibandingkan dengan hasil estimasi langsung (direct) dan prosedur ML.

scholarly journals Small Area Estimation of Smoke-free Workplace Polices and Home Rules in U.S. Counties

2021 ◽  
Author(s):  
Benmei Liu ◽  
Isaac Dompreh ◽  
Anne M Hartman
Keyword(s):  
Tobacco Control ◽  
Small Area ◽  
Small Sample Size ◽  
Health Hazard ◽  
Small Area Estimation ◽  
Small Sample ◽  
County Level ◽  
Area Estimation ◽  
Model Based ◽  
Workplace Policies

Abstract Background The workplace and home are sources of exposure to secondhand smoke (SHS), a serious health hazard for nonsmoking adults and children. Smoke-free workplace policies and home rules protect nonsmoking individuals from SHS and help individuals who smoke to quit smoking. However, estimated population coverages of smoke-free workplace policies and home rules are not typically available at small geographic levels such as counties. Model-based small area estimation techniques are needed to produce such estimates. Methods Self-reported smoke-free workplace policies and home rules data came from the 2014-2015 Tobacco Use Supplement to the Current Population Survey. County-level design-based estimates of the two measures were computed and linked to county-level relevant covariates obtained from external sources. Hierarchical Bayesian models were then built and implemented through Markov Chain Monte Carlo methods. Results Model-based estimates of smoke-free workplace policies and home rules were produced for 3,134 (out of 3,143) U.S. counties. In 2014-2015, nearly 80% of U.S. adult workers were covered by smoke-free workplace policies, and more than 85% of U.S. adults were covered by smoke-free home rules. We found large variations within and between states in the coverage of smoke-free workplace policies and home rules. Conclusions The small-area modeling approach efficiently reduced the variability that was attributable to small sample size in the direct estimates for counties with data and predicted estimates for counties without data by borrowing strength from covariates and other counties with similar profiles. The county-level modeled estimates can serve as a useful resource for tobacco control research and intervention. Implications Detailed county- and state-level estimates of smoke-free workplace policies and home rules can help identify coverage disparities and differential impact of smoke-free legislation and related social norms. Moreover, this estimation framework can be useful for modeling different tobacco control variables and applied elsewhere, e.g., to other behavioral, policy, or health related topics.

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

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.

scholarly journals A New Calibration Estimator of Population Mean for Small Area with Nonresponse

2021 ◽  
pp. 41-51
Author(s):  
J. Iseh Matthew ◽  
J. Bassey Kufre
Keyword(s):  
Coefficient Of Variation ◽  
Small Area ◽  
Distance Measure ◽  
Mean Squared Error ◽  
Small Area Estimation ◽  
Reliable Estimate ◽  
Suitable Alternative ◽  
Population Mean ◽  
Area Estimation ◽  
Unit Nonresponse

This paper considered the challenges of population mean estimation in small area that is characterized by small or no sample size in the presence of unit nonresponse and presents a calibration estimator that produces reliable estimates under stratified random sampling from a class of synthetic estimators using calibration approach with alternative distance measure. Examining the proposed estimator relatively with existing ones under three distributional assumptions: normal, gamma, and exponential distributions with percent average absolute relative bias, percent average coefficient of variation, and average mean squared error as evaluation criteria using simulation analysis technique, the new estimator exhibited a more reliable estimate of the mean with less bias and greater gain in efficiency. Further evaluation using coefficient of variation under varying nonresponse rates to validate the results of variations suggests that the estimator is a suitable alternative for small area estimation. This finding has therefore contributed to the development of an ultimate estimator for small area estimation in the presence of unit nonresponse.

Expenditure Per Capita Model with Spatial Small Area Estimation

2021 ◽  
Vol 1 (2) ◽  
pp. 38-47
Author(s):  
Ahmad Risal
Keyword(s):  
Small Area ◽  
Spatial Information ◽  
Small Area Estimation ◽  
Random Effect ◽  
Development Program ◽  
Data Availability ◽  
Estimation Model ◽  
Policy Makers ◽  
Area Estimation ◽  
Direct Estimation

Indonesia is one of many countries around the world that attempt to suffer from high poverty rates. Since, poverty information in a certain area is a point of interest to researchers and policy makers. One problem faced is for the development program to be carried out more effectively and efficiently, it is necessary to have data availability up to the micro-scale. The technique used to reach the goal is Small Area Estimation (SAE). Fay-herriot (FH) model is one method on Small Area Estimation. Since, the SAE techniques require “borrow strength” across neighbor areas so thus Fay-Herriot model approach was developed by integrating spatial information into the model. This method known as Spatial Fay-Herriot Model (SFH) or Spatial Empirical Best Linear Unbiased Prediction (SEBLUP). This study aims to compare MSE of direct estimation, FH, and SFH Model to see which method gives the best result in estimating expenditure. The MSE value of the estimated SFH is smaller than direct estimation and FH, but it does not significant. It means adding spatial information in the small area estimation model does not give a better prediction than the simple small area estimation which is takes account the area as a specific random effect.

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