Estimator Ridge-Spline Truncated pada Regresi Nonparametrik Multivariabel

'Adhimah, Nila Muhaimatul (2025) Estimator Ridge-Spline Truncated pada Regresi Nonparametrik Multivariabel. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penelitian ini berfokus pada pengembangan dan pengkajian estimator regresi nonparametrik ridge-spline truncated, yaitu pendekatan gabungan antara regresi nonparametrik spline truncated dan regresi ridge yang dirancang untuk menangani bentuk hubungan yang tidak linier sekaligus mengatasi permasalahan multikolinearitas antar variabel prediktor. Kajian teoritis dan aplikatif mengenai estimator ini masih sangat terbatas di literatur. Oleh karena itu, penelitian ini memberikan kontribusi teoritis melalui perumusan dan evaluasi kinerja estimator ridge-spline truncated dalam konteks regresi nonparametrik. Estimasi parameter dilakukan menggunakan metode Maximum Likelihood Estimation (MLE). Pemilihan kombinasi jumlah knot dan nilai penalti ridge-spline truncated optimal menggunakan pendekatan Generalized Cross Validation (GCV). Penelitian ini menggunakan fungsi spline truncated linier dengan jumlah knot dibatasi antara 1 hingga 3 per variabel, dan nilai penalti ridge-spline truncated dibatasi dalam rentang 0,001 hingga 0,003. Sebagai bentuk implementasi praktis, estimator ridge-spline truncated yang telah dirumuskan akan diterapkan untuk memodelkan rata-rata pengeluaran per kapita rumah tangga di 38 kabupaten/kota Provinsi Jawa Timur. Model dikonstruksi berdasarkan lima variabel sosial ekonomi, yaitu Rata-rata Lama Sekolah (RLS), Indeks Pembangunan Manusia (IPM), tingkat pengangguran terbuka (TPT), persentase pemilik jaminan kesehatan BPJS PBI, dan laju pertumbuhan ekonomi. Hasil analisis menunjukkan bahwa model terpilih diperoleh pada kombinasi titik knot (1,2,1,1,1) dengan nilai penalti ridge-spline truncated 0,001889. Model tersebut menghasilkan nilai GCV minimum sebesar 0,00895 serta koefisien determinasi (R²) sebesar 96,72%. Temuan ini menunjukkan bahwa estimator ridge-spline truncated memberikan hasil estimasi yang baik dalam menggambarkan pola hubungan yang kompleks antara rata-rata pengeluaran per kapita rumah tangga dan kelima variabel prediktor yang dipilih, serta mampu mengatasi adanya multikolinieritas antar variabel prediktor.
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This research focuses on the development and assessment of the ridge-spline truncated nonparametric regression estimator, a combined approach between truncated spline and ridge regression, designed to handle nonlinear relationships while addressing multicollinearity among predictor variables. Theoretical and applied studies on this estimator are still very limited in literature. Therefore, this research provides a theoretical contribution by formulating and evaluating the performance of the ridge-spline truncated estimator in the context of nonparametric regression. Parameter estimation was performed using the Maximum Likelihood Estimation (MLE) method. The optimal combination of knots and ridge-spline truncated penalty values was selected using the Generalized Cross Validation (GCV) approach. In this case, a linear truncated spline function was used, with the number of knots limited to 1 to 3 per variable, and the ridge-spline truncated penalty value limited to 0.001 to 0.003. As a practical implementation, this estimator was applied to model average per capita household expenditure in 38 districts/cities in East Java Province. The model was constructed based on five socioeconomic variables, averages years of schooling, the Human Development Index, the open unemployment rate, the coverage of BPJS PBI health insurance, and the economic growth rate. The analysis results show that the selected model is obtained at a combination of knot points (1,2,1,1,1) with a ridge-spline truncated penalty value of 0,001889. The model produces a minimum GCV value of 0,00895 and a coefficient of determination (R²) of 96.72%. These findings indicate that the ridge-spline truncated estimator provides good estimation results in describing the complex relationship pattern between average household per capita expenditure and the five selected predictor variables and is able to handling of multicollinearity between predictor variables.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Generalize Cross Validation, Multikolinearitas, Pengeluaran per Kapita Rumah Tangga, Regresi Nonparametrik Ridge-Spline Truncated Generalize Cross Validation, Household Expenditure per Capita, Multicollinearity, Nonparametric Ridge-Spline Truncated Regression.
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation. Logistic regression analysis. H Social Sciences > HA Statistics > HA31.7 Estimation
Divisions:	Faculty of Mathematics, Computation, and Data Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	Nila Muhaimatul 'adhimah
Date Deposited:	05 Aug 2025 03:24
Last Modified:	05 Aug 2025 03:24
URI:	http://repository.its.ac.id/id/eprint/127202

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