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All Journal Prosiding Seminar Nasional MIPA JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Jurnal Sains dan Seni ITS Mandalika Mathematics and Educations Journal
I Nyoman Budiantara
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Arts Humanities Education Mathematics

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The Estimation of Residual Variance in Nonparametric Regression Abdul Wahab; I Nyoman Budiantara; Kartika Fitriasari
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 3 (2021): May, 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v17i3.13192

Abstract

Given a nonparametric regression model Yi = g(xi) + ei, i = 1, 2, …, n, where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows: . The biased value of residual variance estimator of the Rice method is: , where and. Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is: , Where , , , , , k = 1, 2, … , m. Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.
Faktor-Faktor Yang Mempengaruhi Contraceptive Prevalence Rate (Cpr) Di Indonesia Dengan Pendekatan Regresi Nonparametrik Spline Diana Cristie; I Nyoman Budiantara
Jurnal Sains dan Seni ITS Vol 4, No 1 (2015)
Publisher : Lembaga Penelitian dan Pengabdian Kepada Masyarakat (LPPM), ITS

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2742.124 KB) | DOI: 10.12962/j23373520.v4i1.9234

Abstract

Salah satu permasalahan krusial yang terkait dengan kependudukan berkaitan dengan target MDGs 2015 adalah semakin meningkatnya jumlah penduduk dan tingginya laju pertumbuhan penduduk. Program Keluarga Berencana (KB) merupakan salah satu usaha pemerintah dalam mengendalikan jumlah penduduk. Ukuran yang digunakan untuk mengevaluasi keberhasilan program KB adalah angka prevalensi pemakaian kontrasepsi (CPR). Penelitian ini bertujuan untuk mengetahui faktor-faktor yang mempengaruhi CPR. Pendekatan regresi nonparametrik spline digunakan karena dapat mengestimasi data yang tidak memiliki pola tertentu. Regresi spline yang dipilih adalah yang memiliki titik knot optimum dengan nilai GCV minimum, yaitu tiga titik knot. Berdasarkan hasil pengujian parameter diketahui faktor-faktor yang berpengaruh terhadap CPR adalah persentase penduduk miskin, persentase wanita berumur 15 tahun ke atas dengan pendidikan tertinggi kurang atau sama dengan SLTP, persentase wanita berumur 10 tahun ke atas dengan usia perkawinan pertama 18 tahun ke bawah, persentase wanita berumur 10 tahun ke atas  yang pernah kawin dengan anak lahir hidup kurang atau sama dengan dua, dan persentase wanita berumur 15 tahun ke atas yang bekerja. Model regresi nonparametrik spline ini mempunyai koefisien determinasi ( sebesar 95,59 persen.
PENELITIAN BIDANG REGRESI SPLINE MENUJU TERWUJUDNYA PENELITIAN STATISTIKA YANG MANDIRI DAN BERKARAKTER I Nyoman Budiantara
Prosiding Seminar Nasional MIPA 2011: PROSIDING SEMINAR NASIONAL MIPA UNDIKSHA 2011
Publisher : Prosiding Seminar Nasional MIPA

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Abstract

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The Curve Estimation Nonparametric Regression Multiresponse Mixed with Truncated Spline, Fourier Series, and Kernel Sukran, Ade Matao; I Nyoman Budiantara; Vita Ratnasari
Mandalika Mathematics and Educations Journal Vol 7 No 2 (2025): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i2.9188

Abstract

This study formulates a nonparametric regression model for multiresponse data by combining three estimators: truncated spline, Fourier series, and kernel function. Each estimator captures specific characteristics. Truncated spline capture local traits with knot points, while fourier series capture periodic patterns and kernel estimators provide flexible smoothing for unknown functional forms. The model proposed is under an additive assumption where each predictor contributes independently to each response. Estimation is done with Weighted Least Squares (WLS) method which is efficient in managing the correlations between the multiresponse variables. The final multiresponse nonparametric regression curve estimator combining truncated spline, Fourier series, and kernel is given by \\hat{\mu} = \hat{f} + \hat{g} + \hat{h}\] obtained by solving the WLS optimization problem: [\min_{\boldsymbol{\beta}, \boldsymbol{\alpha}} \{ \boldsymbol{\varepsilon}' W \boldsymbol{\varepsilon} \} =\min_{\boldsymbol{\beta}, \boldsymbol{\alpha}} \left\{ (\mathbf{y}^* - U \boldsymbol{\beta} - Z \boldsymbol{\alpha})' W (\mathbf{y}^* - U \boldsymbol{\beta} - Z \boldsymbol{\alpha}) \right\}.\]. The solution to this problem results in the mixed estimator, which can be expressed as: \[\hat{\boldsymbol{\mu}} = E \mathbf{y} \quad \text{with} \quad E = UB + ZA + T.\]
A Computatioal Analysis of Kernel-Based Nonparametric Regression Applied to Poverty Data Adrianingsih, Narita Yuri; Dani, Andrea Tri Rian; I Nyoman Budiantara; Dandito Laa Ull; Raditya Arya Kosasih
Mandalika Mathematics and Educations Journal Vol 7 No 3 (2025): Edisi September
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i3.9802

Abstract

This research aims to model the relationship between poverty and socioeconomic variables in Nusa Tenggara Timur Province, Indonesia. The purpose of the study is to assess the effectiveness of nonparametric regression, specifically using kernel methods, to provide a more accurate representation of the complex and nonlinear relationships between predictor variables and poverty levels. The study focuses on several key variables, including average years of schooling, labor force participation rate, percentage of households with access to electricity, population density, illiteracy rate, and life expectancy. The research utilized a kernel regression approach, comparing the performance of different kernel functions, including Gaussian, Epanechnikov, Triangle, and Quartic kernels. The model’s performance was evaluated using metrics such as Mean Squared Error (MSE), Generalized Cross Validation (GCV), and the coefficient of determination (R²). The results showed that the Gaussian kernel function provided the most accurate predictions for poverty levels, with the best balance between model complexity and error.
Co-Authors Abdul Wahab Dandito Laa Ull Dani, Andrea Tri Rian Diana Cristie Kartika Fitriasari NARITA YURI ADRIANINGSIH Raditya Arya Kosasih Sukran, Ade Matao Vita Ratnasari