PENDEKATAN METODE PEMULUSAN KERNEL PADA PENDUGAAN AREA KECIL (SMALL AREA ESTIMATION)

Pendugaan area kecil merupakan pendugaan parameter suatu area yang lebih kecil dengan memanfaatkan informasi dari luar area, dari dalam area itu sendiri, dan dari luar survei. Berdasarkan peubah penjelas yang digunakan, terdapat dua model area kecil, yaitu basic area level model dan basic unit level model, dimana kedua model tersebut mengasumsikan bahwa penduga langsung memiliki hubungan yang linier dengan peubah penjelas. Ada kalanya asumsi tersebut tidak dapat dipenuhi dan salah satu solusinya adalah dengan menggunakan pendekatan nonparametrik, seperti pemulusan Kernel. Simulasi yang telah dilakukan menunjukkan bahwa pemulusan Kernel dapat mereduksi bias pendugaan pada pola hubungan yang tidak linier dengan berbagai jumlah area. Nilai Mean Square Error (MSE) pendugaan area kecil dengan menggunakan pemulusan Kernel pada pola hubungan yang tidak linier relatif lebih kecil dibandingkan metode parametrik yang menggunakan model Fay-Herriot. MSE pada pemulusan Kernel memiliki kecenderungan semakin kecil jika jumlah area semakin banyak. Kata Kunci : nonparametrik, pendugaan area kecil, pemulusan Kerne

A COMPARISON OF COX PROPORTIONAL HAZARD AND RANDOM SURVIVAL FOREST MODELS IN PREDICTING CHURN OF THE TELECOMMUNICATION INDUSTRY CUSTOMER

The Cox Proportional hazard model is a popular method to analyze right-censored survival data. This method is efficient to use if the proportional hazard assumption is fulfilled. This method does not provide an accurate conclusion if these assumptions are not fulfilled. The new innovative method with a non-parametric approach is now developing to predict the time until an event occurs based on machine learning techniques that can solve the limitation of CPH. The method is Random Survival Forest, which analyzes right-censored survival data without regard to any assumptions. This paper aims to compare the predictive quality of the two methods using the C-index value in predicting right-censored survival data on churn data of the telecommunication industry customers with 2P packages consisting of  Internet and TV, which are taken from all customer databases in the Jabodetabek area. The results show that the median value of the C-index of the RSF model is 0.769, greater than the median C-index value of the CPH model of 0.689. So the prediction quality of the RSF model is better than the CPH model in predicting the churn of the telecommunications industry customer

Small Area Estimation on Zero-Inflated Data Using Frequentist and Bayesian Approach

The most commonly used method of small area estimation (SAE) is the empirical best linear unbiased prediction method based on a linear mixed model. However, it is not appropriate in the case of the zero-inflated target variable with a mixture of zeros and continuously distributed positive values. Therefore, various model-based SAE methods for zero-inflated data are developed, such as the Frequentist approach and the Bayesian approach. Both approaches are compared with the survey regression (SR) method which ignores the presence of zero-inflation in the data. The results show that the two SAE approaches for zero-inflated data are capable to yield more accurate area mean estimates than the SR method

Overdispersion study of poisson and zero-inflated poisson regression for some characteristics of the data on lamda, n, p

Poisson distribution is one of discrete distribution that is often used in modeling of rare events. The data obtained in form of counts with non-negative integers. One of analysis that is used in modeling count data is Poisson regression. Deviation of assumption that often occurs in the Poisson regression is overdispersion. Cause of overdispersion is an excess zero probability on the response variable. Solving model that be used to overcome of overdispersion is zero-inflated Poisson (ZIP) regression. The research aimed to develop a study of overdispersion for Poisson and ZIP regression on some characteristics of the data. Overdispersion on some characteristics of the data that were studied in this research are simulated by combining the parameter of Poisson distribution (λ), zero probability (p), and sample size (n) on the response variable then comparing the Poisson and ZIP regression models. Overdispersion study on data simulation showed that the larger λ, n, and p, the better is the model of ZIP than Poisson regression. The results of this simulation are also strengthened by the exploration of Pearson residual in Poisson and ZIP regression

EBLUP METHOD OF TIME SERIES AND CROSS-SECTION DATA FOR ESTIMATING EDUCATION INDEX IN DISTRICT PURWAKARTA

Since decentralisation was implemented in Indonesia, more detailed information about the condition of an area becomes very necessary to know as an evaluation of development that the government has done. the success development of a region can be seen through the Human Development Index (HDI). HDI consists of three basic dimensions, knowledge as one of that three basic measured by the index of education. This index is measured by the Adult Literacy Rate and Mean Years of Schooling. Education is one of the important factors in improving human development. The enhancement of education index results in increasing the HDI of an area. Purwakarta has a vision that is made as a district that excels in education in West Java, but until now Purwakarta’s education index is still below the West Java province. One step that can be done is to seek information on the education index each district in Purwakarta, with the aim to provide the right policy in each region. Direct estimation of the components forming the HDI for districts is not feasible because these estimates will generate a great value of variance, This is due to the size of the sample used is too small. This study proposes a statistical method by performing the estimation using small area estimation. These estimates using information from surrounding areas that can improve the effectiveness of the sample size and the lower the standard error. Some surveys are conducted regularly every year, in conducting indirect estimation in the survey such as this, efficiency of estimating education index for district level can be improved by including the random effect of the area as well as the random effect of time (Sadik and Notodipuro, 2006). So in this study will be used Empirical Best Linear Unbiased Prediction (EBLUP) by combining the time series and cross-section data for estimating the education index at the level of districts in Purwakarta. The direct estimation of education index produce a larger variance than our methode, it shown by comparing mean square error (MSE) of direct method and indirect method, direct method have the largest MSE.Key words : Indirect Estimation, Small Area Estimator, EBLUP, Time Series and Cross-Section, HDI, Education Index

TRANSFER FUNCTION AND ARIMA MODEL FOR FORECASTING BI RATE IN INDONESIA

Fluctuating gold prices can have an impact on various sectors of the economy. Some of the impacts of rising and falling gold prices are inflation, currency exchange rates, and the value of the Bank Indonesia benchmark interest rate (BI Rate). The data was taken from the Indonesian Central Statistics Agency's official website (BPS) for the Bank Indonesia benchmark interest rate (BI Rate) value. Therefore, research on the value of the Bank Indonesia benchmark interest rate (BI Rate) is essential with the gold price as a control. The purpose of this study is to forecast the value of the Bank Indonesia reference interest rate (BI Rate) with a transfer function model where the input variable used is the price of gold and forecast the value of the Bank Indonesia benchmark interest rate (BI Rate) with the ARIMA model. The analysis results show that the best model for forecasting the Bank Indonesia reference interest rate (BI Rate) is a transfer function model with a value of , , , and a noise series model  with the MAPE value i

A SIMULATION STUDY OF LOGARITHMIC TRANSFORMATION MODEL IN SPATIAL E MPIRICAL BEST LINEAR UNBIASED PREDICTION (SEBLUP) METHOD OF SMALL AREA ESTIMATION

There have been many studies developed to improve the quality of estimates in small area estimation (SAE). The standard method known as EBLUP (Empirical Unbiased Best Linear Predictor) has been developed by incorporating spatial effects into the model. This modification of the method was known SEBLUP (Spatial EBLUP) since it incorporates the spatial correlations which exist among the small areas. The data obtained (variables of concern) usually have a large variance and tend to have a a nonsymmetric distribution and therefore tend to have nonlinear relationship pattern between concomitant variables and variables of concern. the results showed that the method SEBLUP using logarithmic transformation produces estimator more than the other methods.Keywords : EBLUP, SAE, SEBLU

METODE E-BLUP DALAM SMALL AREA ESTIMATION UNTUK MODEL YANG MENGANDUNG RANDOM WALK

Ada dua topik utama yang menjadi perhatian para statistisi dalam membahas persoalan survei. Yaitu persoalan pengembangan teknik penarikan contoh (sampling technique) dan pengembangan metodologi pendugaan parameter pupulasi (estimation methods). Adapaun persoalan mutakhir dalam metodologi pendugaan adalah menyangkut pendugaan untuk daerah atau domain survei yang memiliki contoh kecil atau bahkan tidak memiliki contoh satupun, Rao(2003). Misalnya survei untuk unit rumah tangga pada suatu survei berskala nasional. Umumnya untuk survei demikian banyaknya contoh rumah tangga untuk tiap kabupaten dalam suatu propinsi sangat kecil (small area). Bahkan bisa terjadi kabupaten tertentu tidak terpilih sebagai daerah survei sehingga contoh rumah tangga dari kabupaten tersebut tidak ada. Metode pendugaan langsung (direct estimation) untuk daerah atau kabupaten yang bersangkutan menjadi tidak layak karena contohnya terlalu kecil. Pada makalah ini akan dipaparkan metode pendugaan daerah kecil (small area estimation) dengan pendekatan pendugaan tidak langsung berbasis model (indirect estimation - model based). Khususnya untuk model yang mengandung langkah acak (random walk).   Kata Kunci :    direct estimation, indirect estimation, generalized regression, general linear mixed model, empirical best linear unbiased prediction, block diagonal covariance, random walk

Proporsi Kemiskinan di Kabupaten Bogor

Kemiskinan merupakan salah satu permasalahan mendasar yang menjadi pusat perhatian pemerintahIndonesia. Aspek penting untuk mendukung strategi penanggulangan kemiskinan adalah ketersediaandata dan informasi yang akurat. Penelitian ini bertujuan untuk menduga proporsi status kemiskinan rumahtangga pada tingkat kecamatan di Kabupaten Bogor dan mengidentifikasi sumber/jenis pekerjaan rumahtangga. Metode yang disusun berdasarkan pendugaan langsung dengan asumsi metode sampel acaksederhana untuk memperoleh penduga proporsi dan berdasarkan tabulasi silang untuk mengetahui latarbelakang jenis pekerjaan yang berdampak pada kemiskinan. Penelitian ini menggunakan data sekunderberupa Survei Sosial Ekonomi Nasional (Susenas) dengan variabel terpilih. Badan Pusat Statistik memilikiprogram pengumpulan data melalui sensus dan survei. Survei tersebut menggunakan metode rancanganpenarikan sampel yang kompleks. Hasil penelitian menunjukkan bahwa rumah tangga miskin di KabupatenProporsi Kemiskinan di Kabupaten Bogor, Titin Suhartini, Kusman Sadik, dan Indahwati 161Bogor sebesar 6,84%. 31,08% rumah tangga miskin berasal dari jenis pekerjaan pertanian tanaman pangan.Hanya 24 kecamatan yang dapat dilakukan pendugaan proporsi status kemiskinan rumah tangga.Pendugaanproporsi rumah tangga miskin terbesar berada di kecamatan Nanggung yaitu sebesar 45%. Untuk mengatasiketerbatasan pendugaan yang dilakukan terhadap 16 kecamatan lainnya dapat menggunakan alternatifmetode pendugaan area kecil

The Study of Small Area Estimation Using Oversampling and M-Quantile Robust Regression Approach

Statistics Indonesia (BPS) calculates poverty indicators (Head Count Ratio, Poverty Gap, and Poverty Severity) using National Socio-Economic Survey (Susenas). Susenas is only designed to estimate province and municipality/regency area level, whereas the government requires estimation until smaller area level (sub-district and village). Estimating poverty indicators directly from Susenas for the smaller area often leads to inaccurate estimates. To solve this problem, BPS usually conduct additional survey called Regional Socio-Economic Survey (Suseda) by increasing number to the original sample (called oversampling) but with the very high cost. Therefore, we proposed small area estimation technique which based on the unit level model using Population Census 2010 (SP2010) as the population auxiliary variables and household per-capita expenditure (Susenas 2015) as the response variable. We utilized robust M-quantile regression model which robust to the outlier using three weight functions (Huber, Hampel, and Tukey Bisquare). Our results provide evidence that M-quantile model is more accurate than direct estimates with oversampling