Judul: Metode Prediksi Tak-bias Linear Terbaik dan Bayes Berhirarki untuk Pendugaan Area Kecil Berdasarkan Model State Space [DISERTASI]
Abstrak: There have been two main topics developed by statisticians in a survey, i.e. sampling techniques and estimation methods. The current issues are estimation methods related to estimation of a particular domain having small size of samples or, in more extreme cases, there is no sample available for direct estimation. Sample survey data provide effective reliable estimators of totals and means for large area and domains. But it is recognized that the usual direct survey estimator for a parameter of small area, have unacceptably large standard errors, due to the circumstance of small sample size in the area. The most commonly used models for this case, usually in small area estimation, are based on generalized linear mixed models. Some time happened that some surveys are carried out periodically so that the estimation could be improved by incorporating both the area and time random effects. In this dissertation we propose a state space model which accounts for the two random effects and is based on two equations, namely transition equation and measurement equation. Based on an evaluation criterion, the proposed hierarchical Bayes estimator turns out to be superior to both estimated best linear unbiased prediction (BLUP) and the direct survey estimator. The posterior variances which measure accuracy of the hierarchical Bayes estimates are always smaller than the corresponding variances of the BLUP and the direct survey estimates
Keyword: Generalized linear mixed model, Best Linear Unbiased Prediction (BLUP), Block Diagonal Covariance, State space model, Prior and posterior function

Judul: Spatial Bayesian Model in Small Area Estimation with Binary Response (Case: Estimation of Poor Families Proportion in Jember, East Java)
Abstrak: suatu subpopulasi dengan ukuran contoh kecil. Metode yang dikembangkan dalam pendugaan area kecil adalah metode pendugaan tidak langsung dengan memanfaatkan kekuatan area di sekitarnya dan sumber data di luar area. Tujuan dari metode pendugaan ini adalah untuk meningkatkan keefektifan ukuran contoh dan menurunkan keragaman dugaan parameter. Model-model dalam pendugaan area kecil mengasumsikan bahwa pengaruh acak galat area saling bebas. Namun dalam beberapa kasus, asumsi ini sering dilanggar. Pelanggaran asumsi ini disebabkan oleh keragaman suatu area dipengaruhi area sekitarnya, sehingga efek spasial dapat dimasukkan ke dalam pengaruh acak. Efek spasial merupakan hal yang lazim terjadi antara satu area dengan area yang lain, ini berarti bahwa area yang satu mempengaruhi area lainnya. Dalam statistika, model yang dapat menjelaskan hubungan antara suatu area dengan area sekitarnya adalah model spasial. Topik utama penelitian ini adalah membentuk model spasial Bayes pada pendugaan area kecil dengan model Logit-Normal yang akan diterapkan pada data kemiskinan. Tema yang diusung dalam penelitian ini yaitu pendugaan proporsi keluarga miskin di Kabupaten Jember Provinsi Jawa Timur. Penelitian ini akan menggunakan peubah respon yang menyebar menurut Binomial (Logit) dan pengaruh area yang menyebar menurut distribusi Normal. Hal ini yang mendasari pemakaian Model Logit-Normal. Tujuan utama yang ingin dicapai dalam penelitian ini, yaitu (1) Mengembangkan metode Bayes berhirarki khusus untuk data peubah respon biner dengan menambahkan pengaruh spasial, (2) mengkaji sifat statistik/penduga parameter proporsi berdasarkan metode Bayes berhirarki, dan (3) menerapkan metode pendugaan area kecil melalui pendekatan Bayes berhirarki untuk menentukan proporsi keluarga miskin di Kabupaten Jember Provinsi Jawa Timur. Studi kasus dilakukan pada dua sumber data, yaitu simulasi dan Susenas Kabupaten Jember Jawa Timur. Data simulasi digunakan untuk mengetahui berbagai karakteristik pendugaan pada beberapa pembobot spasial yang berbeda pada model Logit-Normal Bayes berhirarki berdasarkan pendugaan area kecil. Data kedua adalah data proporsi keluarga miskin untuk desa/kelurahan di Kabupaten Jember Jawa Timur. Data ini merupakan data Survei Sosial-Ekonomi Nasional (Susenas) 2008 yang berbasis rumah tangga serta data Potensi Desa (PODES) 2008 sebagai sumber data pendukung. Hasil simulasi dalam penelitian ini menunjukkan bahwa pada model Logit- Normal Bayes berhirarki dengan pembobot spasial tetangga terdekat dan pembobot spasial korelasi merupakan model terbaik bila dibandingkan dengan model Logit-Normal Bayes berhirarki dengan pembobot spasial jarak dan tanpa pembobot spasial. Hal ini ditunjukkan dengan nila rata-rata RMSE dan persentase bias relatif masing-masing model tersebut kecil., Small area estimation is a method to estimate parameters in a subpopulation with small sample size. The method is based on indirect estimation using the strength of the surrounding area and data sources outside the area to obtain statistic with adequate precision. Generally, the models in small area estimation assumes that the influence of random errors are independent area. However in somecases, this assumption is often violated. This is due to the variance of area which is affected by its neighborhood, so that spatial effect can be incorporated into random area effects. Rao (2003) stated that Logit-Normal model was one of the model in small area estimation which was affected by the spatial effect. It was used to estimate the proportion using Hierarchical Bayes (HB) method. The first objective of this research is to develope
Keyword: proportion of Hierarchical Bayes, the proportion of poor families, spatial weighted, Logit-Normal model, small area estimation

Judul: Pengaruh Jumlah Bahan Pretanning dan Minyak Biji Karet (Hevea brasiliensis) Terhadap Mutu Kulit Samoa. Di
Abstrak: Animal hides or skins are the most valuable by product of the meat industry. Most of those hides are converted into leather by leather tanning process. Chrome based tanning is the most popular tanning process. At the chrome based tanning process, a lot of amount chrome are throw away into the environment that make a significant effect to the biological and ecological environment damaged. Due to concerns over the use and disposal of chromed tanned leather, the leather industry is now facing increasing scrutiny over its use of chrome as tanning agent. The use of non-chrome tannages has gradually become pre-eminent to producing leather, particularly in the European automotive leather markets. Chamois leather is one of leather product. It is produced from animal hides/skins by oil tanning process, usually with fish oil. High price and odour problems to the chamois leather that produced using fish oil motivate to do some research to solve that problems. Rubber seed oil is an oil that predicted can substitute fish oil. Pretanning process is needed to increase the oil penetration and protects the pelt from putrefying during oxidation periods (Khrisnan et al., 2005). Relugan GT 50 is the agent that used on this research. Relugan GT 50 is an aldehyde tanning agent, produced by BASF. This research was aimed to find out the effects of Relugan GT 50 concentration (offer) and rubber seeds (Hevea brasiliensis) oil to the chamois leather’s quality. Beside that, this research is also aimed to decide the best combination of the factors to produce chamois leather also to know the chamois leather characteristics. The preliminary research was carried out by analyzing the rubber seed’s kernel and eggshell as well as physico-chemical properties of the rubber seed oil. The main research was done by tanning the skin with Relugan GT 50 in concentrations of 1.5, 3.0 and 4.5% followed by rubber seed oil concentrations of 10, 20, and 30%. The experimental design used was completely randomize factorial design. The preliminary research shows that rubber seed’s kernel was 49% and rubber seed’s eggshell was 51%. The rubber seed’s oil characterstics were density of 0.94 (g/cm3), viscosity of 48,4 centistokes, colour of 2713 PtCo units, inodine value 113 g iod/ 100 g, peroxide value of 24 miliequivalent/1000 gram oil, acid value of 15 mg KOH/g oil and FFA content of 5.8%. The research shows that Relugan GT 50 concentration significantly affected shrinkage temperature (Ts) and pH; rubber seed oil concentration significantly affect the organoleptic properties of the leather. The optimum conditions for the tanning were Relugan GT of 3.0% concentration and 10% rubber seeds oil. The physical properties of the leather were shrinkage temperature of 75oC, thickness of 0.92 mm, tensile strength of 21.50 N/mm2, elongation at break of 144%, tear strength of 55.77 N/mm, water absorption of 266% (2 hours) and 299% (24 hours). The chemical properties were oil content of 2.5%, ash content of 1.2% and pH of 8. The organoleptic properties were softness of 7–8, colour of 8-9, and odour of 8-9.
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