NONLINEAR PRINCIPAL COMPONENT ANALYSIS AND PRINCIPAL COMPONENT ANALYSIS WITH SUCCESSIVE INTERVAL IN K-MEANS CLUSTER ANALYSIS

K-Means Cluster is a cluster analysis for continuous variables with the concept of distance used is a euclidean distance where that distance is used as observation variables which are uncorrelated with each other. The case with the type data that is correlated categorical can be solved either by Nonlinear Principal Component Analysis or by making categorical data into numerical data by the method called successive interval and then used Principal Component Analysis. By comparing the ratio of the variance within cluster and between cluster in poverty data of East Nusa Tenggara Province in K-Means cluster obtained that Principal Component Analysis with Successive interval has a smaller variance ratio than Nonlinear Principal Component Analysis. Variables that take effect to the clusterformation are toilet, fuel,and job.Keywords: K-Means Cluster Analysis, Nonlinear Principal Component Analysis, Principal Component Analysis, Successive interval

ADVECTION-DIFFUSION MODEL WITH TIME DEPENDENT FOR AIR POLLUTANTS DISTRIBUTION IN UNSTABLE ATMOSPHERIC CONDITION

Air pollution levels are quite high in urban areas. They are emitted from various sources and have an impact on humans and the environment. There are some physical processes that occur when pollutants disperse in the atmosphere. The main processes are advection and diffusion. Therefore, a two-dimensional mathematical model is presented to study the dispersion of air pollution under the effect of mesoscale wind as an effect of urban heat islands. This model is solved by using the implicit Crank-Nicolson finite difference scheme under stability-dependent meteorological parameters involved in large scale wind, mesoscale wind and eddy diffusivity. The main goal of this research is to analyze air pollution distribution using the advection-diffusion model. The results of this model have been analyzed for the dispersion of air pollutants in an urban area in the downwind and vertical direction for unstable atmospheric conditions.Key words : Advection, Diffusion, Mesoscale Wind, Pollutant Dispersio

DETEKSI DINI RISIKO KREDIT MELALUI RATING TRANSITION STOCHASTIC MATRIX DAN VALUE AT RISK (Early Detection of Credit Risk Through Rating Transition Stochastic Matrix and Value at Risk)

Credit risk is the risk occurs when the debtors fail to meet their obligation in accordance with agreed term to the bank. This research is made to analyze the credit risk for industrial and trade sector in Bank X, both sectors contribute about 80% loan credit. The calculation of the VaR 95% used Markov Chain regular and ergodic and adjusted by macro economic variable which significance influence the movement of those quality rating. The result of Markov chain for industrial sector show that the ability debtor increase for repay the loan in the long run but for trade sector became worst. The VaR 95% results for industrial sector is Rp 2,17 billion or about 3,27% and for trade sector is Rp 4,46 billion or about 2,03% from outstanding credit those sectors. This results is not appropriate with the New Basel Capital Accord which recomennded to allocate capital 8% from outstanding credit to cover credit risk. The calculation of the TVaR 95% for industrial sector is Rp 4,89 billion or about 7,38% and for trade sector is Rp 16,60 billion or about 7,55% from outstanding credit both sectors. For the TVaR 95% portofolio give the results is Rp 18,99 billion or about 6,5% from outstanding credit.Keywords : Credit Risk, Markov chain, Regression, Macroeconomics, VaR, TVaR, Portofolio Risk

BOOTSTRAP PARAMETRIK DAN NONPARAMETRIK UNTUK PENDUGAAN KUADRAT TENGAH GALAT DALAM STATISTIK AREA KECIL DENGAN RESPON BERSEBARAN LOGNORMAL

Small area estimation is needed to obtain information in small area, that is area containing small size of sample. Direct estimation in small area will result in large variance. Indirect estimation is the solution, with involves auxiliary data from related area or another survey in parameter estimation. One of the prolems found in using this procedure is low precision of Mean Square Error (MSE) estimate caused by non-normal distribution. Parameter of concern in this study is per capita expenditure of village in Bogor regency. Per capita expenditure is non-normal distribution. MSE estimator with bootstrap method has the advantage of potential robustness against sampling from non- normal distribution. Therefore this study used bootstrap method, such as parametric bootstrap and nonparametric bootstrap, in MSE estimation. Generally, the result showed that the MSE estimate of the parametric bootstrap smaller than the nonparametric bootstrap. Both method have better precision, so that they can repair the result of direct estimation.Keywords : small area estimation, parametric bootstrap, nonparametric bootstra

Penerapan Multivariate Cusum Time Series untuk Mendeteksi Kegagalan Bank di Indonesia

Bank merniliki peran penting dalam pengalokasian sumberdaya keuangan. Kondisi bank yangtidak sehat dapat menyebabkan bank tidak dapat menjalatzkan peran tersebut, sehingga akanmenghanlbat kelancaran akt$tas perekonomian nasional. Dalam mengevaluasi kinerja bank,beberapa pendekatan metodologi terutama metodologi statistik telah banyak dilakukan. Nalnunselama ini nzetodologi tersebut tidak mengikutsertakan perilaku deret waktu dari peubah-;7eubahnya. Padahal peubah-peubah keuangan suatu perusahaan secara serial berkorelasi tinggi.Tulisan ini bertujuan untuk mendeteksi kegagalan bank dengan menggunakan multivariatecztsunz tiine series.Model kegagalan bank yang dibangun oleh multivariate clrsunz time series, cukup mampu dalanzrnendeteksi adanya gejala memburuk pada kondisi kesehatan bank. Hal ini sejalan dengansenzangat pendeteksian krisis perbankan secara dini (early warning banking crises).Kata kunci : Multivariate Cusum Time Series, Kegagalan Ban

PENDEKATAN KUADRAT TERKECIL PARSIAL KEKAR UNTUK PENANGANAN PENCILAN PADA DATA KALIBRASI

The serious problems in the calibration of multivariate estimation are multicollinearity and outliers. Partial Least Squares (PLS) is one of the statistical method used in chemometrics, to handle high or perfect multicollinearity in independent variables. Straightforward Implementation Partial Least Squares (SIMPLS) is the extension of PLS regression proposed by De Jong (1993). The SIMPLS algorithm is based on the empirical cross-variance matrix between the independent variables and the regressors. This method does not resistant toward outlier observations. Robust PLS method is used to handle the multicollinearity and outliers in the data sets. This method can be classified in two groups, there are iteratively reweighting technique and robustication of covariance matrix. Partial Regression-M (PRM) method is one of the robust PLS methods used the idea of iteratively reweighting technique that proposed by Serneels et al. (2005). Robust SIMPLS (RSIMPLS) method is one of the robust PLS methods used the idea of robustication of covariance that proposed by Huber and Branden (2003). A modified RSIMPLS used M estimator with the Huber weight function called RSIMPLS-M was proposed by Ismah (2010). These two methods (RSIMPLS-M and PRM) are applied to Fish data (Naes 1985) to know their performances. The research results indicated that the values of R2 and RMSEP of RSIMPLS-M are higher than those of PRM method. Whereas based on the confidence interval estimation of the regression coefficients by jackknife method, estimation of PRM is narrower than that RSIMPLS-M method. Therefore RSIMPLS-M method is better than PRM method for prediction, whereas PRM method is better than RSIMPLS-M method for estimation.Keywords : Partial least squares regression robust (PLSRR), partial robust M-regression (PRM), straightforward implementation partial least squares robust (RSIMPLS

GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) INCLUDED THE DATA CONTAINING MULTICOLLINEARITY

One of the reasons of spatial effect of each location is spatial variety. Beside of spatial variety, number of independent variable (X) causes local multicolinearity, that is one or more independent variable, which collaborated with other variable in each location of observation. The methods can be used to solve spatial diversity problem and local multicollinearity in Geographically Weighted Regression (GWR) model that is GWPCA. This research aim to examine GWPCAR feasibility model for PDRB data in 2010 at 113 districts/cities in Java. analysis indicate that GWPCA method can overcome local multicollinearity problem, it can be seen from the characteristic value of VIF which is smaller than 10.Key words : Local Multicollinearity, Geographically Weighted Principal Components Analysis

MODEL AVERAGING, AN ALTERNATIVE APPROACH TO MODEL SELECTION IN HIGH DIMENSIONAL DATA ESTIMATION

Model averaging is an alternative approach to classical model selection in model estimation. The model selection such as forward or stepwise regression, use certain criteria in choosing one best model fitted the data such as AIC and BIC. On the other hand, model averaging estimates one model whose parameters determined by weighted averaging the parameter of each approximation models. Instead of conducting inference and prediction only based one best chosen model, model averaging covering model uncertainty problem by including all possible model in determining prediction model. Some of its developments and applications also challenges will be described in this paper. Frequentist model averaging will be preferential described.Keywords : model selection, frequentist model averaging, high dimensional dat

RANDOM PARAMETER MODELS OF FERTILIZER RESPONSE FOR CORN USING SKEWED DISTRIBUTIONS

Random parameter models have been found to better determine the optimum dose of fertilizer than fixed parameter. However, a major restriction of it is the normality assumption.. The purpose of this study the introduction of random parameter models of fertilizer response using skewed distributions from a Bayesian perspective. The method is applied to data sets of multilocation trials of potassium fertilization on corn. We compare the Linear Plateau, Spillman-Mitscherlich, and Quadratic random parameter models with different random errors distribution assumption, i.e. as normal, skew-normal, Student-t and Skew-t distribution using the Deviance Information Criterion (DIC). The results show that the smallest DIC value is obtained for the normal linear plateau model compare with the other models. The correlation between observed and fitted values was significant.Key words : fertilizer response model, mixed effects, skewed distributions, DIC

AUTOREGRESSIVE MOVING AVERAGE (ARMA) MODEL FOR DETECTING SPATIAL DEPENDENCE IN INDONESIAN INFANT MORTALITY DATA

Infant mortality is an important indicator that must to be monitored seriously. The infant mortality is associated with several determinants, such as the infant’s characteristics, maternal and fertility factors, housing condition, geographical area, and policy. It can also be influenced by the presence of spatial dependence between regency in Indonesia. This is due to the social and economic activity in one regency depend on social and economic activity in other regency, especially with neighboring area. Infant mortality data obtained from Indonesian Demographic and Health Survey (IDHS) published by Statistic Indonesia (BPS). In BPS’s publication, data is always sorted by regency code from the smallest to the largest. Therefore, the closeness of the regency code refers to the closeness of the regency itself. the infant mortality data by regency could be analogized as time series data. So that, the relationship between regency can be seen using Autoregressive Moving Average (ARMA) model. If the parameter at ARMA is significant, we can conclude that there is a spatial dependence on the infant mortality in Indonesia. This paper will focus on discussing whether there is a spatial dependenc in Indonesia’s Infant Mortality Data using ARMA approach. The result is the Autocorrelation Function (ACF) showed a significant effect until lag 3, and Partial Autocorrelation Function (PACF) showed a significant effect until lag 1. Based on Bayesian Information Criterion (BIC), the AR(1) fitted the model well. It shows that the probability of infant mortality in one regency is affected by probability of infant mortality in neighboring regency.Key words : ARMA, spatial dependence, infant mortality, IDH