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Review Jurnal Terkait
Matriks Varians-
Kovarians
Judul
Estimation of Regression Function
in Multi-Response
Nonparametric Regression
Model Using Smoothing Spline
and Kernel Estimators
Jurnal
Journal of Physics :
Conference Series.
1097 (1)
Tahun
2018
Penulis
• Budi Lestari
• Fatmawati
• I Nyoman
Budiantara
• Nur Chamidah
Dalam artikel ini membahas tentang bagaimana
mengestimasi fungsi regresi dari model regresi
nonparametrik multirespon dengan menggunakan
estimator smoothing spline dan kernel. Tujuan utamanya
adalah menentukan estimator smoothing spline dan
kernel untuk mengestimasi fungsi regresi dari model
regresi nonparametrik multirespon.
Pendekatan regresi nonparametrik cocok digunakan untuk pola
data yang bentuk kurva regresinya tidak diketahui. Regresi
nonparametrik dikembangkan dalam beberapa estimator seperti
spline, kernel, fourier, wavelet dan polinomial lokal. Telah banyak
penelitian yang membahas mengenai regresi nonparametrik
menggunakan estimator spline dan kernel, namun penelitian-
penelitian tersebut masih melibatkan satu respon dalam model
regresi. Dalam artikel ini akan dibangun model regresi
nonparametrik multirespon dengan menggunakan estimator
smoothing spline dan kernel untuk memperkirakan fungsi regresi
dari model regresi nonparametrik multirespon.
1. Estimation of Regression Function Using Spline Smoothing
Estimator
dengan matriks pembobot , dalam kasus ini matriks merupakan matriks varians kovarians sebagai
berikut:
Matriks pembobot ini kemudian dilibatkan dalam pengestimasian dengan menggunakan metode PWLS dan
RKHS sehingga diperoleh:
2. Estimation of Regression Function Using Kernel Estimator
dengan menggunakan rata-rata terboboti dari raw data diperoleh :
kemudian diperoleh estimasi sebagai berikut :
Kesimpulan
Berdasarkan hasil estimasi yang diperoleh, estimator smoothing spline dan kernel
linear dalam pengamatan dan merupakan estimator bias untuk fungsi regresinya.
Estimator smoothing spline dan kernel secara matematis hanya dibedakan oleh
matriks penghalus. Dalam pendekatan menggunakan estimator spline smoothing,
matriks penghalus merupakan matriks simetris dan bergantung pada dan titik
knot. Sedangkan pada estimator kernel menggunakan matriks penghalus kernel.

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Review.pptx

  • 1. Review Jurnal Terkait Matriks Varians- Kovarians
  • 2. Judul Estimation of Regression Function in Multi-Response Nonparametric Regression Model Using Smoothing Spline and Kernel Estimators Jurnal Journal of Physics : Conference Series. 1097 (1) Tahun 2018 Penulis • Budi Lestari • Fatmawati • I Nyoman Budiantara • Nur Chamidah
  • 3. Dalam artikel ini membahas tentang bagaimana mengestimasi fungsi regresi dari model regresi nonparametrik multirespon dengan menggunakan estimator smoothing spline dan kernel. Tujuan utamanya adalah menentukan estimator smoothing spline dan kernel untuk mengestimasi fungsi regresi dari model regresi nonparametrik multirespon.
  • 4. Pendekatan regresi nonparametrik cocok digunakan untuk pola data yang bentuk kurva regresinya tidak diketahui. Regresi nonparametrik dikembangkan dalam beberapa estimator seperti spline, kernel, fourier, wavelet dan polinomial lokal. Telah banyak penelitian yang membahas mengenai regresi nonparametrik menggunakan estimator spline dan kernel, namun penelitian- penelitian tersebut masih melibatkan satu respon dalam model regresi. Dalam artikel ini akan dibangun model regresi nonparametrik multirespon dengan menggunakan estimator smoothing spline dan kernel untuk memperkirakan fungsi regresi dari model regresi nonparametrik multirespon.
  • 5. 1. Estimation of Regression Function Using Spline Smoothing Estimator dengan matriks pembobot , dalam kasus ini matriks merupakan matriks varians kovarians sebagai berikut: Matriks pembobot ini kemudian dilibatkan dalam pengestimasian dengan menggunakan metode PWLS dan RKHS sehingga diperoleh:
  • 6. 2. Estimation of Regression Function Using Kernel Estimator dengan menggunakan rata-rata terboboti dari raw data diperoleh : kemudian diperoleh estimasi sebagai berikut :
  • 7. Kesimpulan Berdasarkan hasil estimasi yang diperoleh, estimator smoothing spline dan kernel linear dalam pengamatan dan merupakan estimator bias untuk fungsi regresinya. Estimator smoothing spline dan kernel secara matematis hanya dibedakan oleh matriks penghalus. Dalam pendekatan menggunakan estimator spline smoothing, matriks penghalus merupakan matriks simetris dan bergantung pada dan titik knot. Sedangkan pada estimator kernel menggunakan matriks penghalus kernel.