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ASYMPTOTIC APPROXIMATIONS TO THE BIAS AND VARIANCE OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND Mangku, I Wayan
Journal of the Indonesian Mathematical Society Volume 17 Number 1 (April 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.1.8.1-9

From the previous research, a kernel-type estimator of the intensity ofthe cyclic Poisson process with the linear trend has been constructed using a singlerealization of the Poisson process observed in a bounded interval. This proposedestimator has been proved to be consistent as the size of the observation intervaltends to innity. In this paper, asymptotic approximations to its bias, variance andMSE (Mean-Squared-Error) are computed. Asymptotically optimal bandwidth isalso derived.DOI :Â http://dx.doi.org/10.22342/jims.17.1.8.1-9

CONSISTENCY OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND Mangku, I Wayan; -, Siswadi; Budiarti, Retno
Journal of the Indonesian Mathematical Society Volume 15 Number 1 (April 2009)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.15.1.42.37-48

A consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window in definitely expands.DOI :Â http://dx.doi.org/10.22342/jims.15.1.42.37-48

ESTIMATION OF UNEMPLOYMENT RATE USING SMALL AREA ESTIMATION MODEL BASED ON A ROTATING PANEL NATIONAL LABOR FORCE SURVEY Siti Muchlisoh; Anang Kurnia; Khairil Anwar Notodiputro; I Wayan Mangku
FORUM STATISTIKA DAN KOMPUTASI Vol. 20 No. 2 (2015)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (421.543 KB)

In Indonesia, labor force participation data are collected by Sakernas (National Labor Force Survey). Sakernas is conducted based on a quarterly rotating panel survey. Because of the groups differ according to their time-in-panel and observation strategy, it is possible to the presence of a bias. Besides, there are insufficiency problem of sample size to obtain an adequate precision of direct estimation at the district level. It is necessary to study how to estimate parameter based on a rotating panel survey when sample size is insufficient. Currently, a small area estimation (SAE) model that accomodates the bias component due to the rotation still only assume the effect over time which follows a random walk process, so it is necessary to develop a model that is more general. We propose a SAE model for rotation group level, its combined idea of the time-series multi-level model and the Rao-Yu model. The model will applied to Sakernas data to estimate a quarterly unemployment rate at the district level.Key words : Sakernas, rotating panel survey, time-series multi-level model and Rao-Yu model

MODEL AVERAGING, AN ALTERNATIVE APPROACH TO MODEL SELECTION IN HIGH DIMENSIONAL DATA ESTIMATION Deiby T. Salaki; Anang Kurnia; Arief Gusnanto; I Wayan Mangku; Bagus Sartono
FORUM STATISTIKA DAN KOMPUTASI Vol. 20 No. 2 (2015)
Publisher : FORUM STATISTIKA DAN KOMPUTASI

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (541.415 KB)

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 data

Penentuan Metode Terbaik Uji Kalium untuk Tanaman Tomat Pada Tanah Inceptisols Luthfi Izhar; Anas D Susila; Bambang S Purwoko; Atang Sutandi; Iwayan Mangku
Jurnal Hortikultura Vol 23, No 3 (2013): September 2013
Publisher : Indonesian Center for Horticulture Research and Development

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21082/jhort.v23n3.2013.p218-224

Penelitian tentang studi analisis kalium tanah dan aplikasi pupuk kalium pada budidaya tomat pada tanah Inceptisols dilakukan di Kebun Percobaan dan Rumah Kaca di Cikabayan, Institut Pertanian Bogor, dari Bulan April hingga November 2011. Tujuan penelitian untuk mendapatkan metode ekstraksi kalium tanah yang terbaik guna menentukan dosis pupuk kalium pada budidaya tomat pada tanah Inceptisols. Penelitian menggunakan rancangan acak kelompok dengan perlakuan pemberian pupuk kalium pada beberapa tingkat dosis, yaitu 0, ¼, ½, ¾, dan 1X, dimana nilai X ialah 608,6 kg K O kg/ha dengan empat ulangan. Perlakuan pemupukan kalium diterapkan pada 3 bulan sebelum penanaman tomat. Analisis korelasi dilakukan antara kandungan K tanah dan pertumbuhan tanaman di dalam rumah kaca menggunakan media inkubasi berasal dari tanah setelah diberi perlakuan. Uji kalium tanah menggunakan lima metode ekstraksi, yaitu metode HCl 25%, NH422) OAc 1 M pH 7, Mehlich I, Truog, dan Morgan Vanema. Hasil penelitian menunjukkan perbedaan yang nyata antara pengaruh perlakuan pupuk K terhadap parameter tinggi tanaman, jumlah daun, dan diameter batang tomat. Bobot segar biomassa dan bobot kering tomat juga menunjukkan perbedaan pengaruh yang nyata antarperlakuan. Nilai korelasi tertinggi ditunjukkan pada metode pengekstrak Truog melalui parameter bobot kering dan basah relatif tanaman (r = 0,7). Dengan demikian, uji K tanah menggunakan metode Truog dapat digunakan sebagai metode ekstraksi yang paling tepat untuk menganalisis unsur hara kalium dalam rangka penyediaan rekomendasi pemupukan K pada budidaya tomat pada tanah Inceptisols.

Empirical Bayesian Method for the Estimation of Literacy Rate at Sub-district Level Case Study: Sumenep District of East Java Province A.Tuti Rumiati; Khairil Anwar Notodiputro; Kusman Sadik; I Wayan Mangku
IPTEK The Journal for Technology and Science Vol 23, No 1 (2012)
Publisher : IPTEK, LPPM, Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j20882033.v23i1.13

This paper discusses Bayesian Method of Small Area Estimation (SAE) based on Binomial response variable. SAE method being developed to estimate parameter in small area due to insufficiency of sample. The case study is literacy rate estimation at sub-district level in Sumenep district, East Java Province. Literacy rate is measured by proportion of people who are able to read and write, from the population of 10 year-old or more. In the case study we used Social Economic Survey (Susenas)data collected by BPS. The SAE approach was applied since the Susenas data is not representative enough to estimate the parameters at sub-district level because it’s designed to estimate parameters in regional area (in scope of a district/city at minimum). In this research, the response variable being used was logit function trasformation of pi (the parameter of Binomial distribution). We applied direct and indirect approach for parameter estimation, both using Empirical Bayes approach. For direct estimation we used prior distribution of Beta distribution and Normal prior distribution for logit function (pi) and to estimate parameter by using numerical method, i.e integration Monte Carlo. For indirect approach, we used auxiliary variables which are combinations of sex and age (which is divided into five categories). Penalized Quasi Likelihood (PQL) was used to get parameter estimation of SAE model and Restricted Maximum Likelihood method (REML) for MSE estimation. Instead of Bayesian approach, we are also conducting direct estimation using classical approach in order to evaluate the quality of the estimators. This research gives some findings, those are: Bayesian approach for SAE model gives the best estimation because having the lowest MSE value compares to the other methods. For the direct estimation, Bayesian approach using Beta and logit Normal prior distribution give a very similar result to the direct estimation with classical approach since the weight of is too large, which is about 0.905. It is also found that direct estimation using Bayesian approach with the Beta prior distribution gives better MSE than using logit normal prior distribution.

Analisis Kemiskinan Menggunakan Model Panel Spasial Statik Jajang Jajang; Asep Saefuddin; I Wayan Mangku; Hermanto Siregar
MIMBAR (Jurnal Sosial dan Pembangunan) Volume 29, No. 2, Year 2013 [Accredited by Ristekdikti]
Publisher : Universitas Islam Bandung

The purpose of this research is to study the effects of GDP, population, employment of junior high school graduated, employment shares of agriculture, industry, trading and services to the number of poor people in Central Java Province. The method used to this modeling is spatial modeling. The results of research show that when GDP, employment shares of industry, trading and services are increase, the number of poor people is decrease. However, when the population, employment share of agriculture and employment of junior high school graduated are increase, the number of poor people is increase. Based on these findings there are some policies should be implemented to reduce the number of poor people, such as improvement of economic growth, improvement of education, controlling the population and employment transformation from agricultural sector to industry, trading and services sectors.

ASYMPTOTIC APPROXIMATIONS TO THE BIAS AND VARIANCE OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND I Wayan Mangku
Journal of the Indonesian Mathematical Society Volume 17 Number 1 (April 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.1.8.1-9

From the previous research, a kernel-type estimator of the intensity ofthe cyclic Poisson process with the linear trend has been constructed using a singlerealization of the Poisson process observed in a bounded interval. This proposedestimator has been proved to be consistent as the size of the observation intervaltends to innity. In this paper, asymptotic approximations to its bias, variance andMSE (Mean-Squared-Error) are computed. Asymptotically optimal bandwidth isalso derived.DOI : http://dx.doi.org/10.22342/jims.17.1.8.1-9

CONSISTENCY OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND I Wayan Mangku; Siswadi -; Retno Budiarti
Journal of the Indonesian Mathematical Society Volume 15 Number 1 (April 2009)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.15.1.42.37-48

A consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window in definitely expands.DOI : http://dx.doi.org/10.22342/jims.15.1.42.37-48

Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk Auliya Fithry; I Wayan Mangku; I Gusti Putu Purnaba
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 and to do a simulation study to observe the probabilities that parameters are contained in the confidence intervals. We do not assume any parametric form for the intensity function except that it is periodic. We consider in the observed there is only one realization of the cyclic Poisson process in a bounded interval. The main results are two theory about confidence intervals for parameters. The simulation shows that the probability values of the observed parameters contained in the confidence intervals are in accordance with the theory.

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