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I Nyoman Budiantara
Departemen Statistika Institut Teknologi Sepuluh Nopember
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Journal : Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)

 1 
MATRIKS KOVARIANSI DALAM REGRESI NONPARAMETRIK MULTIRESPON PADA KASUS KORELASI SAMA DAN KORELASI TIDAK SAMA Budi Lestari; I Nyoman Budiantara; Sony Sunaryo; Muhammad Mashuri
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 4 No 1 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2012.4.1.2950

Abstract

In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.
MATRIKS KOVARIANSI DALAM REGRESI NONPARAMETRIK MULTIRESPON PADA KASUS KORELASI SAMA DAN KORELASI TIDAK SAMA Budi Lestari; I Nyoman Budiantara; Sony Sunaryo; Muhammad Mashuri
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 4 No 1 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2012.4.1.2950

Abstract

In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.
Co-Authors Achmad Zubaydi Agnes Tuti Rumiati Anita Trias Anggraeni Ayu Febriana Dwi Rositawati Ayu Ukhti Mufidah Ayuk Putri Sugiantari Azizah Azizah Bagiyo Suwasono Bagiyo Suwasono Bagiyo Suwasono, Bagiyo Bambang Widjanarko Otok Benny Kusuma Budi Lestari Budi Lestari Camelia Nanda Sholicha Chairunnisa, Nurul Rizky Crespo, Mohamad Dani, Andrea Dani, Andrea Tri Rian Delila Ramadanti Bidari Dewi Wahyu Setyowati Dhira Audhia Pratiwi Eko Wahyu Wibowo Elfrida Kurnia Litawati Erma Oktania Permatasari Errina Dwi Igustin Fadhlul Rahim Febriyani, Eka Riche Firda Fahrun Nisa' Fitriana, Dewi Fortano, Nauvalla Farhan Putra Fredi Suryadi Fredi Suryadi Hadianti, Wafirah Putri Hesikumalasari Hesikumalasari I Dewa Ayu Made Istri Wulandari I Gusti Putu Surya Darma Inggar Putri Merdekawati Irma Wahyu Rosanti Irma Yahya Ismaini Zain Kartika Fitriasari Khaerun Nisa' Krisna Wulandari Latifatul Mubarokah Lilik Hidayati, Lilik Ludia Ni’matuzzahroh M. Fariz Fadillah Mardianto Made Ayu Dwi Octavanny Madu Ratna Merly Fatriana Bintariningrum Meyda Arynta muhammad mashuri Nalim Nalim Ni Putu Dera Yanthi Nisa', Khaerun Novalia Dwita Pramitasari Novia Asri Kurniawati Nur Chamidah Nuraini, Ulfa Siti Nuraziza Arfan Nuroini, Husna Mir'atin Nurul Fajriyyah Nurul Fitriyani Nurul Izzah Nym Cista Striratna Dewi Octavianta Romauli Sitanggang Patrica Pungky Gabrela Permatasari, Erma Oktania Puspita Khanela Putra, Fachrian Bimantoro Putri, Asyifa Charmadya Ramadhani, Riska Kunti Ratri Galuh Pramesti Reza Mubarak Riana Kurnia Dewi Rifani Nur Sindy Setiawan Rizkiana Prima Rahmadina Robiatul Maziyah Ruli Sartika Sari Sherly Mega Tri Marina Shofa F Nisai Sifriyani, Sifriyani Siti Nasfirah Sjarief Widjaja Sony Sunaryo Sony Sunaryo Suryo Guritno Suryo Guritno Tavio, Tavio Vita Ratnasari Wiyli Yustanti Zaed Yuliadi Zaed Yuliadi, Zaed