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All Journal Journal of the Indonesian Mathematical Society Jurnal Pembelajaran Berpikir Matematika JURNAL ILMIAH MATEMATIKA DAN TERAPAN Sebatik Indonesian Journal of Health Sciences Research and Development (IJHSRD) 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 Health Professions Law, Crime, Criminology & Criminal Justice Mathematics Public Health 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.
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
MODEL-CHECKS FOR HOMOSCHEDASTIC SPATIAL LINEAR REGRESSION MODEL BASED ON BOOTSTRAP METHOD Wayan Somayasa
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 7 No. 2 (2010)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2010.v7.i2.138

Abstract

In  this  paper  we  propose  Efron  residual  based-bootstrap  approximation  methods in  asymptotic  model-checks  for  homoschedastic  spatial  linear  regression  models.  It  is  shown  that  under  some  regularity conditions given to the known regression functions the bootstrap version of the sequence of least squares residual partial sums processes converges in distribution to a centred Gaussian process having sample paths in the space of continuous functions on  1,0 1,0 :I . Thus, Efron residual based-bootstrap is a consistent approximation in the usual sense. The finite sample performance of the bootstrap level   Kolmogorov-Smirnov (KS) type test is also investigated by means of Monte Carlo simulation.
ESTIMASI PARAMETER DAN UJI GOODNESS OF FIT UNTUK DATA BINER BERPASANGAN: ESTIMASI PARAMETER DAN UJI GOODNESS OF FIT Ummi Maryam; Wayan Somayasa; Ruslan Ruslan; La Gubu La Gubu; Jufra Jufra
Jurnal Matematika Komputasi dan Statistika Vol. 2 No. 1 (2022): Januari - April
Publisher : Universitas Halu Oleo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (779.67 KB) | DOI: 10.33772/jmks.v2i1.7

Abstract

Tujuan penelitian ini adalah menunjukkan estimasi parameter dan uji goodness of fit untuk data biner berpasangan. Estimasi parameter dilakukan menggunakan metode estimasi maksimum likelihood. Data biner dari organ berpasangan diperoleh dengan melakukan pengukuran dari bagian tubuh yang berpasangan atau dari subjek yang sama pada dua titik waktu yang berbeda. Dengan asumsi adalah hasil pengukuran bagian tubuh ke dari bagian tubuh yang berpasangan dari subjek ke dan kelompok ke . dapat bernilai atau (biner). jika bagian tubuh ke dari bagian tubuh yang berpasangan dari subjek ke dan kelompok ke menunjukkan respond dan jika sebaliknya. Adapun model yang digunakan untuk menggambarkan hasil pengukuran organ berpasangan yaitu model Rosner (1982) dan model Dallal (1988). Rosner (1982) mengusulkan suatu konstanta yang memperhitungkan intra korelasi bagian tubuh yang dipasangkan. Rosner (1982) menyatakan bahwa untuk beberapa konstanta positif . Jika maka bagian tubuh yang dipasangkan independen, jika maka bagian tubuh yang dipasangkan saling dependen. Dallal (1988) mengkritik asumsi Rosner (1982) karena tidak dapat mendekati untuk semua kelompok kecuali nilai hampir sama. Dallal (1988) mengasumsikan . Selanjutnya dilakukan pengaplikasian model Rosner (1982) dan model Dallal (1988) terhadap data pasien scleroderma dimana MRSS (Modified Rodnan Skin Score) digunakan sebagai alat ukur ketebalan kulit yang telah divalidasi oleh American Collage of Rheumatologist. Dari kedua model kemudian dilakukan uji goodness of fit untuk mengetahui alokasi probabilitas kedua model. Selanjutnya dilakukan pemilihan model terbaik menggunakan metode Akaike’s Criterion Information (AIC).
Co-Authors Abidin, Muhammad Abidin, Muhammad Sainal Adami, Aryani Agusrawati Alfian Alfian Alfian Anggita Septiawati Arman 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 Hamrin, La Ode Harnawati Helena Hasti Hermanto Hermanto Iin Sukma Febrianti Ira Ernawati Ismi Febriani Jufra Jufra Jufra Jufra Jufra, Jufra La Gubu 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 Mulia Kasih, Rachmi Dwi Nasrul Niken Nirmala Norma Muhtar Novi Nur Khafifah Nurul Nahdahfajriani Mansyur Nurwijayanti Pimpi, La Radiyatul Mardiyah Rahmalia Sahapati Rahmalia Sahupala Rahmalia Sahupala Reski Amelia Restayani Resti Azari Rita Ayu Ningtyas Roro Anteng Ruslan Ruslan Ruslan Ruslan Ruslan Ruslan Ruslan Sardiani, Rita Sarina Sarjum Bao Siska Andiaga Siti Hapsah, Siti Siti Nurazizah Siti Rahmawatisari Sulmianti Sutiari, Desak Ketut Tongku, Reisaldy Fathi Jafar Ummi Maryam Wa Lisanto