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All Journal Jurnal Matematika 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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Journal : jurnal matematika

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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.
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 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