Judul: Gini Ratio and the Components Prediction based on YbarraLohr Model with Estimated Sampling Variance
Abstrak: Gini ratio is one of the parameters used to measure income inequality, so it is necessary to know the value of the Gini ratio down to the level of smaller areas such as subdistricts. The Gini ratio classification is divided into three, those are very high (0,50 – 0,70), moderate (0,36 -0,49), and low (0,20 – 0,35). The components of the Gini ratio according to BPS for the subdistrict level are the average expenditure per capita and the relative frequency of households for each expenditure class in the subdistrict. Per capita expenditure data available through SUSENAS is designed to obtain national statistics down to the district level, so it is necessary to make estimates for the subdistrict expenditure class level. Direct estimation for small samples can cause large standard errors, therefore small area estimation with Logarithmic Transformation is used as a solution to fulfill the linearity assumption of the model to estimate the average per capita expenditure for each expenditure class for each subdistrict in Depok City in 2020. The expenditure class in this study was determined based on the BPS expenditure class and the distribution of response variable data. The Ybarra-Lohr model at the area level is used due to the availability of accompanying variables at the area level that contain errors which are also available in SUSENAS data. The area is the expenditure class in each subdistrict in Depok City. Estimation was also carried out in one sampleless area in one subdistrict. The sampling variance needed to estimate the average per capita expenditure, is estimated by comparing several methods of estimation, including direct estimation, probability distribution, and bootstrap repetitions of 1000, 10000 and 50000. Estimation of sampling variance and small area estimation analysis using the Ybarra-lohr model and logarithmic transformation done using R software with the help of the saeme package. The method of estimating the model variance with the probability distribution yields an estimate of the average expenditure per capita with the smallest RRMSE, and the random effect variance and the goodness of the YbarraLohr model are σ̂v 2 = 0.686, R 2= 0.929. The results of estimating the best average per capita expenditure for each expenditure class are used to obtain the gini ratio for each subdistrict in Depok City in 2020. Classification is based on the level of inequality, gini ratio with indirect results in all subdistricts in Depok City which are included in the low category are Bojongsari, Pancoran Mas, Cipayung, Sukmajaya, Cilodong, Tapos, Beji, and Limo subdistricts. The subdistricts included in the category of moderate inequality are Sawangan, Cimanggis, and Cinere subdistricts.
Keyword: EBLUP log transform, gini ratio, saeme, sampling variance

Judul: Study on the Effects of Cluster Information in Prediction of Non-sampled Area (A Case Study of per Capita Expenditures at Subdistrict Level in Regency and Municipality of Bogor).
Abstrak: Empirical Best Linear Unbiased Predictor (EBLUP) has been widely used to predict parameters in area with small or even zero sample size, known as non-sampled area. It has been noted that there is a problem when this model will be used to predict the parameters of non-sampled area. Usually EBLUP is used to predict the parameters using a synthetic model ignoring the area random effects due to lack of non-sampled area information. Hence, this prediction will be distorted based on a single line of the synthetic model. The idea developed in this thesis is to modify the prediction model by adding cluster information assuming that there are similiarities among particular areas. These information have been incorporated into the model to modify the intercept of prediction models as well as both intercept and slope of the prediction model. In this paper, a simulation is carried out to study the performance of the proposed models compared with ordinary EBLUP. All models were evaluated based on the value of Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE). It was shown, by mean of simulation, that the addition of cluster information has improved the ability of the model to predict non-sampled areas. Restricted Maximum Likelihood (REML), a common method for estimating variance component in EBLUP models, requires normality assumption. But the conditions in which the area random effects or sampling error are not normally distributed may encountered in many applications. Therefore we also used different scenarios, such as either one of random component was not normally distributed or both of area random effects and sampling error area were not normally distributed, to study the performance of the proposed models when the area random effects or auxiliary variables are not normally distributed. The result showed that under these conditions, the proposed models has been able to estimate the parameter with smaller Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE) than ordinary EBLUP, especially in non-sampled areas. It was shown that all models could be used to predict average per capita expenditures per month at subdistrict level in regency and municipality in Bogor. The analysis was based on SUSENAS 2010 and PODES 2011 data sets. Even though the resulting predictions of the models were different, similar pattern among them has been observed. Clustering technique played an important role in implementing the proposed model in the case study. Clustering pattern which tend not to be linearly correlated with response variable can lead to the result that proposed model was not better than standard EBLUP model. However, there were some proposed models that showed a better accuracy than the standard EBLUP prediction of non-sampled subdistrict parameter.
Keyword: EBLUP, Clustering, Linear Mixed Models

Judul: Embriogenesis ikan buta (Astyanax fasciatus)
Abstrak: Ikan buta Astyanax fasciatus adalah spesies ikan unik dari famili Characidae yang menempati perairan dalam gua di Wilayah La Cueva Chica-San Luis Potasi-Mexico. Ikan ini memiliki mata yang tereduksi (Blind Cavefish) dan warna kulit merah muda, pucat serta mengkilap.
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