Judul: Geoinformatika pada Kasus Area Kecil dan Penerapannya untuk Mendeteksi Kantong-kantong Kemiskinan di Jember
Abstrak: Scan statistic is a method in Geinformatics considering spatial unsure to detect high or low potential area geographically and examine an area proportion parameter compare with others proportion statistically. This method detects extreme area (maximum or minimum) called hotspot. Hotspot means something unusual, anomalies, or critical condition area. Scan statistic is used to detect and evaluate area called Most Likely Cluster (MLC). It needs complete information about detected area with large sample size, while survey usually uses small sample size. One solution to overcome small sample size is by increasing sample size, but it is cost, time, and energy consuming. On the other side, there is a developing method in statistics to use survey data with small sample size, i.e. Small Area Estimation (SAE). Although this method is not used to compare among area, the biggest benefit from SAE is that it can be used to estimate area parameter complete, both surveyed and un-surveyed area. With complete estimation data, scan statistic can be used to detect hotspot or Most Likely Cluster (MLC). Based on the need of complete estimator value, SAE application is necessary in scan statistic. Quality of SAE application result in scan statistic depends on (i) sample size of hotspot, (ii) SAE estimation quality of model with some auxiliary variables and estimation methods, so SAE estimation methods need to be examined. SAE quality in handling small sample size case and scan statistic have been studied separately. This dissertation studies scan statistic in small sample size case, as an application of SAE on scan statistic. Estimation result gained through survey is called as Direct Estimate (DE), but usually with low accuracy and precision. There is a direct estimation proportion in MLC problem in Geoinformatics that can be replaced by estimation through SAE. This study’s purposes are to replace DE role with SAE estimation in Geoinformatics problem (in search for hotspot), to do cluster detection through scan statistic using small sample size by using SAE model into scan statistic, and use small area based Geoinformatics to detect poverty area pockets based on surveyed data and estimation of all village in Jember, East Java. This study is an application of SAE based scan statistic that is examined theoretically, by simulation, and by application on real data. SAE application on scan statistic can handle problems in detecting highly potential and statistically significant by using only small sample size. Simulation and application examination on real data are evaluated using statistic properties. Analysis continues with evaluation of correct classification on result gained. 100% correct classification through simulation examination on surveyed area is gained using Bayes and non-Bayes SAE. Bayes methods used in this study are spatial Hierarchical Bayes (HB) and non-spatial method, while non-Bayes methods used are EBLUP and SEBLUP. In un-surveyed area (large area), MLC will be bigger. HB1 (spatial correlation weighted) with hotspot proportion 0.95 is capable to estimate 80.97% correctly, while HB2 (nearest neighbor) is 75.62%. On the other side, EBLUP is only capable to estimate 65.99% of correct classification. From estimator property side, both methods (HB and EBLUP) have stable on result
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