Judul: Kajian bias metode area-specific jackknife dan bias metode weighted jackknife dalam pendugaan area kecil untuk respon poisson dengan pendekatan bayes
Abstrak: 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 edequate precision. Empirical Bayes (EB) method can be used to obtain estimates of small area parameters. In this paper the method was used to handle count data responses. The quality of an estimate can be measured by mean squared error (MSE). Wan (1999) proposed a weighted jackknife method for finding MSE of EB and showed that weighted jackknife methods have desirable asymptotic properties. The concept of this method is to put weights using hat matrix of auxiliary variables. Rao (2003) proposed a modification of jackknife method described in Jiang et al. (2002). This method leads to a computationally simpler jackknife estimator with an area-specific leading term. In the simulation study for Poisson responses, the relative bias of the area-specific jackknife estimator has been shown as the best MSE estimator in small number of areas for Poisson-Gamma model. For Poisson-Lognormal model, the relative bias of the weighted jackknife estimator has been shown as the best MSE estimator. Finnaly, this method was applied to estimate small area mean squared errors in disease mapping problems.
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Judul: Model bayes untuk pendugaan area kecil dengan penarikan contoh berpeluang tidak sama pada kasus respon binomial dan multinomial
Abstrak: In this research a Bayesian Method of Small Area Estimation (SAE) has been developed based on binomial and multinomial response variables using Susenas data obtained from unequal probability sampling. Case study was carried out to predict education level of the population measured by literacy rate and mean years of schooling in sub-district level in East Java Province. The SAE model for binomial response was developed with two methods, i.e. using weighted logit normal mixed model and involving the probability of sampling selection model as exponential function into the SAE model. A simulation study was carried out by implementing 100 times sampling selection into population data. Penalized Quasi Likelihood (PQL) and Restricted Maximum Likelihood method (REML) was used to parameter estimation of SAE model. Based on the simulation result, we found that the weighted logit normal mixed model gave the best estimate. In application, the weighted logit normal mixed model also provided good prediction of literacy rate in Sumenep and Pasuruan regency.For the multinomial respons, we applied the weighted logit multinomial mixed model. MSE estimation was used Jackknife method and it gave very small MSE of about 1,14 x10-7.
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Judul: Kadar Delstrosa, Levulosa, Maltosa, serta Sukrosa Madu Segar dan Madu Bubuk dengan Bahan Pengisi Campuran Gum Arab dan Delstrin
Abstrak: Madu iilerupakan sumber karbohidrat yang komponen utamanya adalah gula berbentuk monosakarida yaitu levulosa dan dekstrosa. Madu bersifat higroskopis yaitu inenyerap air sehingga dapat menyebabkan kerusakan pada madu berupa fermentasi. Salah satu cara mengawetkan madu adalah pengeringan karena pengeringan dapat menghilangltan sebagian besar air dari madu. Pengeringan juga dapat mempermudah penanganan madu seperti pengemasan, penyimpanan maupun pengangkutannya.
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