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Vita Ratnasari
Jurusan Statistika Institut Teknologi Sepuluh Nopember
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Journal : Jurnal Gaussian

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ESTIMATOR RIDGE-DERET FOURIER PADA REGRESI NONPARAMETRIK Muthahharah, Sidratul; Budiantara, I Nyoman; Ratnasari, Vita
Jurnal Gaussian Vol 15, No 1 (2026): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/j.gauss.15.1.77-88

Abstract

Nonparametric regression is frequently applied to describe the connection between variables when the functional form is not defined. The Fourier series estimator is especially effective in capturing periodic patterns in regression curves. In multivariable cases, however, strong correlations among predictor variables often lead to multicollinearity, which results in unstable parameter estimation due to the near-singularity of the design matrix. While the Fourier approach has been widely developed for curve estimation, its theoretical framework has not explicitly accommodated this issue. This research introduces a ridge–Fourier series estimator for nonparametric regression to achieve stable parameter estimation in the presence of multicollinearity. The estimator is derived under a penalized likelihood framework by incorporating a ridge penalty into the Fourier series model and optimizing it using Maximum Likelihood Estimation (MLE). This approach yields a closed-form estimator with reduced variance and improved numerical stability while retaining the flexibility of the nonparametric structure. The oscillation parameter and ridge penalty parameter are determined through the Generalized Cross Validation (GCV) criterion to achieve an optimal smoothing level. This research's major contribution involves the theoretical formulation and derivation of the ridge–Fourier series estimator within the additive nonparametric regression model.
Co-Authors A. Tuti Rumiati Achmad Choiruddin Adatul Mukarohmah Affandi, Nuraga Isma Agnes Tuti Rumiati Almira Qattrunnada Qurratu'ain Ananda, Dwi Shinta Andrea Tri Rian Dani Anita Susanti Arif Khoirul Anam AVIANTHOLIB, IGAR CALVERIA Bachtiar, Raditya Fahmi Baredwan, Abdullah Husin Bastian, Endhy Bastian, Endhy Budiantara, I Cinde Pristi Kurnia Merdiko Citto Pacama Fajrinia Clara Dewanti Dani, Andrea Tri Rian Deby Lolita Permatasari Dedy Dwi Prastyo Dwi Maumere Putra Eko Wahyu Wibowo Elika Tantri Eling Anindita, Raden Erma Oktania Permatasari Fachrian Bimantoro Putra Farid Achmadi Farony, Rivan Faurizal Limansyah Fauziyah, Meirinda Febriliani Masitoh Feni Ira Puspita, Feni Ira Fithriasari, Kartika Fitriana, Dewi Fuad Achmadi Gita Prestalita Halistin, Halistin Haryono Haryono Hesikumalasari Hesikumalasari Hitapriya Suprayitno, Hitapriya Husna Miratin Nuroini I Nyoman Budiantara I Putu Artama Wiguna Ida Nur Indah Sari Insan Amalia Mutfi Ismaini Zain Karimah, Aprilia Fitri Khaerun Nisa' Ludia Ni’matuzzahroh Made Ayu Dwi Octavanny Madu Ratna Mahendra Wardhana, Mahendra Marshiela, Jessie Reyna Maulidiah Nitivijaya Mokh. Suef Muhammad Aldani Zen Muthahharah, Sidratul NARITA YURI ADRIANINGSIH Ni'matuzzahroh, Ludia Nina Saraswati Nina Saraswati Nisa Andini Noer Aisyah Barlian, Noer Aisyah Novidianto, Raditya Nuroini, Husna Mir'atin Nuroini, Husna Miratin Okka Kusumawati Asmoyo Permatasari, Erma Oktania Pramaningrum, Dea Saraswati Purhadi Purhadi Putra, Fachrian Bimantoro Qonita Qurrota A'yun R Sutjipto Reny Nadlifatin Retno Dewi Yulianti Rhifda Zukhrufi Ria Asih Aryani Soemitro Rifani Nur Sindy Setiawan Rizfanni Cahya Putri Rizky Amalia Yulianti Santi Puteri Rahayu Setiawan Setiawan Shofi Andari Sifriyani, Sifriyani Sitti Imaslihkah Suci Amalia Talmera, Annisa Triana Tandri Patih Taufiqotul Masrukha Tesha Nisva Tiza Ayu Virania Veniola Forestryani Vida Faiza Rochmah Wahyu Indri Astuti Wibawati Wibawati Winarni Kurniasari Yashintia Arien Epriliyanti Yollafie Asmara Yovita Liana Salsabila Yuanita Damayanti Zen, Muhammad Aldani