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All Journal Jurnal Matematika Journal of the Indonesian Mathematical Society Jurnal Pembelajaran Berpikir Matematika JURNAL ILMIAH MATEMATIKA DAN TERAPAN Sebatik Jurnal Pengabdian Masyarakat Ilmu Terapan (JPMIT) Jurnal Matematika, Komputasi dan Statistika Jurnal Pengabdian Masyarakat Singa Podium (JPMSIPO) Bakti Cendekia (Jurnal Ilmiah Multi Disiplin)
Wayan Somayasa
Department Of Mathematics, Universitas Haluoleo
Agriculture, Biological Sciences & Forestry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Electrical & Electronics Engineering Environmental Science Law, Crime, Criminology & Criminal Justice Mathematics Social Sciences

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THE PARTIAL SUMS OF THE LEAST SQUARES RESIDUALS OF SPATIAL OBSERVATIONS SAMPLED ACCORDING TO A PROBABILITY MEASURE Somayasa, Wayan
Journal of the Indonesian Mathematical Society Volume 19 Number 1 (April 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.1.127.23-40

Abstract

A functional central limit theorem for a sequence of partial sums processes of the least squares residuals of a spatial linear regression model in which the observations are sampled according to a probability measure is established. Under mild assumptions to the model, the limit of the sequence of the least squares residual partial sums processes is explicitly derived. It is shown that the limit process which is a function of the Brownian sheet depends on the regression functions and the probability measure under which the design is constructed. Several examples ofthe limit processes when the model is true are presented. Lower and upper bounds for boundary crossing probabilities of signal plus noise models when the noises come from the residual partial sums processes are also investigated.DOI : http://dx.doi.org/10.22342/jims.19.1.127.23-40
ON SET-INDEXED RESIDUAL PARTIAL SUM LIMIT PROCESS OF SPATIAL LINEAR REGRESSION MODELS Somayasa, Wayan
Journal of the Indonesian Mathematical Society Volume 17 Number 2 (October 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.2.4.73-83

Abstract

In this paper we derive the limit process of the sequence of set-indexedleast-squares residual partial sum processes of observations obtained form a spatiallinear regression model. For the proof of the result we apply the uniform central limittheorem of Alexander and Pyke (1986) and generalize the geometrical approach ofBischo (2002) and Bischo and Somayasa (2009). It is shown that the limit processis a projection of the set-indexed Brownian sheet onto the reproducing kernel Hilbertspace of this process. For that we dene the projection via Choquet integral of theregression function with respect to the set-indexed Brownian sheet.DOI : http://dx.doi.org/10.22342/jims.17.2.4.73-83
ON WEAK CONVERGENCE OF THE PARTIAL SUMS PROCESSES OF THE LEAST SQUARES RESIDUALS OF MULTIVARIATE SPATIAL REGRESSION Somayasa, Wayan
Journal of the Indonesian Mathematical Society Volume 20 Number 2 (October 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.2.183.77-94

Abstract

A weak convergence of the sequence of partial sums processes of theresiduals (PSPR) when the observations are obtained from a multivariate spatiallinear regression model (SLRM) is established. The result is then applied in constructingthe rejection region of an asymptotic test of hypothesis based on a type ofCramer-von Mises functional of the PSPR. When the null hypothesis is true, we getthe limit process as a projection of the multivariate Brownian sheet, whereas underthe alternative it is given by a signal plus multivariate noise model. Examples ofthe limit process under the null hypothesis are also studied.DOI : http://dx.doi.org/10.22342/jims.20.2.183.77-94
Perbandingan Uji Likelihood Ratio Dan Uji F Asymtotik Pada Regresi Linier Hermanto, Hermanto; Somayasa, Wayan; Pimpi, La
Jurnal Pembelajaran Berpikir Matematika (Journal of Mathematics Thinking Learning) Vol 5, No 2 (2020)
Publisher : Universitas Halu Oleo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33772/jpbm.v5i2.15032

Abstract

Abstrak: Analisis regresi adalah studi mengenai ketergantungan satu variabel terikat dengan satu atau lebih variabel bebas, dengan tujuan mengestimasi dan memprediksi rata-rata populasi atau nilai rata-rata variabel terikat berdasarkan nilai variabel bebas yang diketahui. Terdapat berbagai uji hipotesis yang dapat digunakan untuk menentukan model yang cocok untuk untuk mengetahui hubungan antar variabel tidak bebas dengan satu atau lebih variabel bebas, di antarannya adalah uji likelihood ratio dan uji F asimtotik. Uji hipotesis menggunakan uji likelihood ratio, dimana merupakan salah satu uji yang berhubungan langsung dengan penduga maksimum likelihood, yang model distribusi dari populasinya mengikuti model distribusi dengan pdf tertentu dimana diasumsikan normal dibandingkan dengan uji hipotesis menggunakan uji F asymtotik, yang merupakan uji di mana perosedur inferensi secara asimtotik tidak membutuhkan asumsi distribusi dari observasinya. uji hipotesis baik uji likelihood ratio dan uji F asymtotik pada analisis regresi menghasilkan bentuk model yang sama.Kata Kunci: Analisis Regresi, Uji Likelihood ratio, Uji F AsymtotikAbstract: Regression analysis is a study of the dependence of one dependent variable with one or more independent variables, with the aim of estimating and predicting the population mean or average value of the dependent variable based on the known value of the independent variable. There are various hypothesis tests that can be used to determine a suitable model to determine the relationship between dependent variables and one or more independent variables, including the likelihood ratio test and the asymptotic F test. Hypothesis testing uses the likelihood ratio test, which is one of the tests that is directly related to the maximum likelihood estimator, where the distribution model of the population follows a distribution model with a particular pdf which is assumed to be normal compared to the hypothesis test using the asymptotic F test, which is a test in which the inference procedure asymptotically it does not require assuming the distribution of the observations. Hypothesis test both likelihood ratio test and asymptotic F test in regression analysis produces the same model.Key words: Regression Analysis, likelihood ratio test, asymptotic F test.
Penataan Desa Berbasis Teknologi Informasi Pada Desa Tanjung Tiram Kecamatan Moramo Utara Djafar, Muh. Kabil; Sani, Asrul; Somayasa, Wayan; Jufra, Jufra; Mukhtar, Norma; Budiman, Herdi
Jurnal Pengabdian Masyarakat Ilmu Terapan (JPMIT) Vol 3, No 2 (2021)
Publisher : Vokasi Universitas Halu Oleo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (405.541 KB) | DOI: 10.33772/jpmit.v3i2.21318

Abstract

Pelaksanaan program kegiatan Pengabdian kepada Masyarakat Terintegrasi Kuliah Kerja Nyata– Tematik (KKN-Tematik) bertujuan untuk meningkatkan efisiensi pelayanan masyarakat, dengan memanfaatkan teknologi informasi dalam bentuk Sistem Informasi Desa bebasis web. Metode pelaksanaan kegiatan ini dengan caramemberikan pelatihan teknologi informasi secara formal dan nonformal kepada masyarakat dan perangkat desa. Hasil dari kegiatan PkM terintegrasi KKNTematik adalah mitra dalam hal ini Desa Tanjung Tiram memiliki Sistem Informasi Desa/Website. Pengelolaan Sistem Informasi Desa dilaksanakan oleh seorang perangkat desa, yang telah mendapat pelatihan teknologi informasi.
Model-Check Based on Residual Partial Sums Process of Heteroscedastic spatial Linear Regression Models Wayan Somayasa
Jurnal Matematika Vol 1 No 2 (2011)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2011.v01.i02.p15

Abstract

It is common in practice to evaluate the correctness of an assumed linear regressionmodel by conducting a model-check method in which the residuals of the observations areinvestigated. In the asymptotic context instead of observing the vector of the residuals directly,one investigates the partial sums of the observations. In this paper we derive a functional centrallimit theorem for a sequence of residual partial sums processes when the observations comefrom heteroscedastic spatial linear regression models. Under a mild condition it is shown thatthe limit process is a function of Brownian sheet. Several examples of the limit processes arealso discussed. The limit theorem is then applied in establishing an asymptotically Kolmogorovtype test concerning the adequacy of the fitted model. The critical regions of the test for finitesample sizes are constructed by Monte Carlo simulation.
BY MEANS OF LINDEBERG’S CENTRAL LIMIT THEOREM WAYAN SOMAYASA
Jurnal Matematika Vol 1 No 1 (2010)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2010.v01.i01.p11

Abstract

We study the construction of a version of standard Brownian sheet called h -generalized standardBrownian sheet. It is shown by means of Lindeberg’s theorem that it is a limit process of a sequence ofpartial sums processes of independent random variables in the sense of weak convergence in the metricspace of continuous functions on the compact region [0,1]×[0,1]. Based on this convergence weapproximate by simulation the quantiles of Kolmogorov, Kolmogorov-Smirnov and Cramér-von Misestype statistics which are defined as continuous functionals of the process.
ON SET-INDEXED RESIDUAL PARTIAL SUM LIMIT PROCESS OF SPATIAL LINEAR REGRESSION MODELS Wayan Somayasa
Journal of the Indonesian Mathematical Society Volume 17 Number 2 (October 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.2.4.73-83

Abstract

In this paper we derive the limit process of the sequence of set-indexedleast-squares residual partial sum processes of observations obtained form a spatiallinear regression model. For the proof of the result we apply the uniform central limittheorem of Alexander and Pyke (1986) and generalize the geometrical approach ofBischo (2002) and Bischo and Somayasa (2009). It is shown that the limit processis a projection of the set-indexed Brownian sheet onto the reproducing kernel Hilbertspace of this process. For that we dene the projection via Choquet integral of theregression function with respect to the set-indexed Brownian sheet.DOI : http://dx.doi.org/10.22342/jims.17.2.4.73-83
THE PARTIAL SUMS OF THE LEAST SQUARES RESIDUALS OF SPATIAL OBSERVATIONS SAMPLED ACCORDING TO A PROBABILITY MEASURE Wayan Somayasa
Journal of the Indonesian Mathematical Society Volume 19 Number 1 (April 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.1.127.23-40

Abstract

A functional central limit theorem for a sequence of partial sums processes of the least squares residuals of a spatial linear regression model in which the observations are sampled according to a probability measure is established. Under mild assumptions to the model, the limit of the sequence of the least squares residual partial sums processes is explicitly derived. It is shown that the limit process which is a function of the Brownian sheet depends on the regression functions and the probability measure under which the design is constructed. Several examples ofthe limit processes when the model is true are presented. Lower and upper bounds for boundary crossing probabilities of signal plus noise models when the noises come from the residual partial sums processes are also investigated.DOI : http://dx.doi.org/10.22342/jims.19.1.127.23-40
ON WEAK CONVERGENCE OF THE PARTIAL SUMS PROCESSES OF THE LEAST SQUARES RESIDUALS OF MULTIVARIATE SPATIAL REGRESSION Wayan Somayasa
Journal of the Indonesian Mathematical Society Volume 20 Number 2 (October 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.2.183.77-94

Abstract

A weak convergence of the sequence of partial sums processes of theresiduals (PSPR) when the observations are obtained from a multivariate spatiallinear regression model (SLRM) is established. The result is then applied in constructingthe rejection region of an asymptotic test of hypothesis based on a type ofCramer-von Mises functional of the PSPR. When the null hypothesis is true, we getthe limit process as a projection of the multivariate Brownian sheet, whereas underthe alternative it is given by a signal plus multivariate noise model. Examples ofthe limit process under the null hypothesis are also studied.DOI : http://dx.doi.org/10.22342/jims.20.2.183.77-94
Co-Authors Abidin, Muhammad Sainal Adami, Aryani Agusrawati Alfian Alfian Andi Tenriawaru Anggita Septiawati Arman Arman Asrul Sani Asrul Sani Asrul Sani Aswani Aswani Aswani Ayudikta Fitri Salaam Baharuddin Bahriddin Budiman, Herdi Christina Desriana Djafar, Muh. Kabil Djafar, Muhammad Kabil Edi Cahyono Eka Sahapati Elga Dwi Suanda Febriani Fifin Siti Indrawati Fitriani Gusti Ngurah Adi Wibawa Harnawati Helena Hasti Hermanto Hermanto Iin Sukma Febrianti Ira Ernawati Ismi Febriani Jufra Jufra Jufra Jufra, Jufra La Gubu La Gubu La Gubu La Ode Saidi La Ode Saidi La Pimpi Lilis Laome Maarif Marni Rezki Mildawati Mohammad Syadam Purwanto Muhammad Indra Alamsyah Muhammad Kabil Djafar Muhammad Kabil Djafar Muhtar, Norma Mukhsar Mukhtar, Norma Nasrul Niken Nirmala Norma Muhtar Novi Nur Khafifah Nurul Nahdahfajriani Mansyur Pimpi, La Rachmi Dwi Mulia Kasih Radiyatul Mardiyah Rahmalia Sahapati Rahmalia Sahupala Rahmalia Sahupala Reisaldy Fathi Jafar Tongku Reski Amelia Restayani Resti Azari Rita Ayu Ningtyas Rita Sardiani Roro Anteng Ruslan Ruslan Ruslan Ruslan Ruslan Ruslan Ruslan Sarina Sarjum Bao Siska Andiaga Siti Hapsah, Siti Siti Nurazizah Siti Rahmawatisari Sulmianti Sutiari, Desak Ketut Ummi Maryam Wa Lisanto