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: Pendugaan Area Kecil untuk Data Lognormal dengan Ketergantungan Spasial antar Area Kecil
Abstrak: The need for accurate statistics is currently increasing, not only for the whole population, but also for some parts (subs) of population. Data from a survey can be used as information source for producing the statistics. Unfortunately, most of surveys are usually designed to produce some statistics for a whole population. Consequently, the survey data is often too small (or could be zero) for producing some statistics by direct estimation method in some subpopulations, especially for those are not planned in the survey. Statistics which are produced by direct estimation method will have large standard error if they are based on very small sample size. Moreover, if the sample size is zero then the statistics by direct estimation method cannot be obtained. The subs of population which the selected sample from it is not large enough for producing reliable direct estimates is known by small area. A statistical method that focuses on estimating some parameters in a small area is called by Small Area Estimation (SAE). To increase the effectiveness of small sample size in small areas, it is necessary to consider indirect estimation method which can be implemented by ‘borrowing strength’, utilizing some information from some resources, such as censuses, surveys or administrative records. Furthermore, ‘borrowing strength’ also could be implemented by exploiting data structures, such as considering the possibility of spatial dependence among small areas. SAE is a method for estimating parameter which is model-based. The standard SAE models, which are usually mixed models, are employed for estimating a linear small area parameter. The model assumes that the variable of interest follows normal distribution and there is no correlation among small areas. This dissertation aims to develop the best predictor of linear small area parameter as well as nonlinear small area parameter whenever the variable of interest follows positively skew distribution and among small areas is spatially correlated. A linear small area parameter is a linear function of the population values of a variable of interest in a given small area. On the other hand, a nonlinear small area parameter is a nonlinear function of the population values of a variable of interest. A total or mean population of a variable of interest in a given small area is an example of linear small area parameter whereas a ratio or quantile is a nonlinear parameter. The estimates of linear small area parameter as well as nonlinear small area parameter are derived under our proposed model, namely a unit-level spatial lognormal mixed model. This model assumes that the variable of interest follows log normal distribution and among small areas are spatially correlated by following Simultaneously Autoregressive (SAR) process. To predict the values of variable of interest for non-sampled units, it has been proposed the spatial synthetic estimator (SYNT) and the Spatial Empirical Best Predictor (SEBP). The SYNT predicts the non-sampled values by its unconditional expectation whereas the SEBP predicts them by its conditional expectation. The conditional expectation for obtaining the SEBP of linear small area parameter is calculated analytically. On the other hand, the conditional expectation for obtaining the SEBP of
Keyword: spatial empirical best predictor, spatial synthetic estimator, linear small area parameter, nonlinear small area parameter, unit-level spatial lognormal mixed model

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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