B-Spline Dan Spline Dalam Regresi Nonparametrik Serta Penerapannya

Suryadi, Fredi (2006) B-Spline Dan Spline Dalam Regresi Nonparametrik Serta Penerapannya. Masters thesis, Institut Teknologi Sepuluh November.

Text 1304201020-Master_thesis.pdf Restricted to Repository staff only Download (19MB)

Abstract

Analisa regresi nonparametrik dengan pendekatan spline truncated sudah tidak asing lagi bagi statistikawan yang sering menggunakan analisa regresi nonparametrik. Namun ada kelemahan dalam pendekatan spline yaitu pada orde tinggi, titik knot yang banyak maupun titik knot yang terlalu dekat akan membentuk persamaan normal dengan matrik yang mendekati singular. Untuk mengatasi hal tersebut, dipakai pendekatan B-spline Hasil kajian estimator koefisien fungsi B-spline adalah
γ = (B(λ)ᵀ B(λ))⁻¹ B(λ)ᵀ y Studi simulasi, nilai MSE pendekatan spline truncated cenderung lebih besar dibanding pendekatan B-spline pada berbagai ukuran sampel, standar deviasi dan berbagai fungsi. Pada ukuran sampel n=50 dan 100 perbedaan itu cenderung semakin jelas dibanding pada ukuran sampel n=250. Dalam tulisan ini juga dilakukan pendekatan B-spline pada data real, tentang pola hubungan nilai ujian masuk dan nilai IPK (Indek Prestasi Kumulatif) mahasiswa jurusan Disain Komunikasi Visual tahun 1999 di Universitas Kristen Petra Surabaya, dan menghasilkan fungsi sebagai berikut : Model B-spline linear : ŷ* = 1,03532 B₀ + 1,14796 B₁ + 1,14943 B₂
=====================================================================================================================================
Nonparametric regression analysis with spline approximation not exclusive for Statisticians. But the basis tends to be ill conditioned which is often manifested in a nearly singular matrix. Among other things, this makes the normal equations difficult to solve. Thus, it is desirable to explore the use of other basis for which are better conditioned. One basis with this property is the B-spline basis. Coefisien estimation B-spline curve is
γ = (B(λ)ᵀ B(λ))⁻¹ B(λ)ᵀ y
The simulation study comparison of Truncated spline and B-spline approximation, result
MSE (Mean Square Error) have chance Truncated spline larger than B-splne at several sample
size, standard deviation and function. For the sample size 50 and 100 have distinct greater than
sample size 250. In this paper is studied application B-spline for nonparametric regression at relation score input examination with Grade Point Average (GPA) from visual communication design student in Petra Chistian University in Surabaya. Result from this application is :
B-spline linear model : ŷ* = 1,03532 B₀ + 1,14796 B₁ + 1,14943 B₂

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.536 Sur b
Uncontrolled Keywords:	B-spline, Regresi nonparametrik, Spline,
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	magang .
Date Deposited:	01 Oct 2026 02:50
Last Modified:	01 Oct 2026 02:50
URI:	http://repository.its.ac.id/id/eprint/145120

Actions (login required)

View Item