Estimasi Kurva Regresi Nonparametrik Pada Data Longitudinal Dengan Pendekatan Spline

Basri, Hasan (2009) Estimasi Kurva Regresi Nonparametrik Pada Data Longitudinal Dengan Pendekatan Spline. Masters thesis, Institut Teknologi Sepuluh November.

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Abstract

Diberikan data longitudinal (t_ij, Y_ij), dengan hubungan antara t_ij dan Y_ij diasumsikan mengikuti model regresi nonparametrik Y_ij = f(t_ij) + e_ij ; j = 1, ..., n_i; i = 1, ..., n. Bentuk kurva regresi f diasumsikan tidak diketahui yang termuat di dalam ruang W_2^m [a,b], dimana estimasi model meggunakan pendekatan spline truncated. Dengan menyelesaikan optimasi Weighted Least Square diperoleh estimator kurva regresi nonparametrik untuk data longitudinal, yaitu f̂ = Ŷ = A[k]Y.

Selanjutnya, diberikan aplikasi untuk menduga kurva hubungan antara waktu (t) dan tegangan kolom beton bertulang mutu normal (Y) yang diukur secara longitudinal. Dalam mengestimasi kurva hubungan ini, secara bersama-sama dapat dibentuk model regresi nonparametrik dengan pendekatan spline. Berdasarkan pada pemilihan titik knot yang optimum, dengan menyertakan bobot W* diperoleh:
Ŷ_ij = 2.3863 t_1j - 1.3752 (t_1j - 6)+ - .6791 (t_1j - 22)+ + 0.6039 (t_1j - 31)+ + 3.4387 t_2j - 1.8527 (t_2j - 4)+ - 3.0626 (t_2j - 17)+ + 1.4184 (t_2j - 23)+ + 4.0628 t_3j - 2.5651 (t_3j - 6)+ - 1.8053 (t_3j - 15)+ + 0.0408 (t_3j - 32)+ + 1.6337 t_4j - 1.8828 (t_4j - 23)+ - 2.2224 (t_4j - 52)+ + 2.2649 (t_4j - 57)+
model ini mempunyai nilai Generalized Cross-Validation (GCV) = 0.0128.
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Let the longitudinal data (t_ij, Y_ij), with related between t_ij and Y_ij assumed the follow nonparametric regression model Y_ij = f(t_ij) + e_ij ; j = 1, ..., n_i; i = 1, ..., n. Regression curve f is assumed unknown be in space of W_2^m [a,b], where the model estimation using spline truncated approach. With solution Weighted Least Square optimisation are obtained nonparametric regression curve estimator for longitudinal data, that is f̂ = Ŷ = A[k]Y. Furthermore, apply to estimate curve of relation between time (t) and normal stress of confined concrete column (Y). The estimation of this relation curve, can be construct nonparametric regression model using spline approach do simultaneously. According optimum knots choosing, with enclose weighted W* obtained: Ŷ_ij = 2.3863 t_1j - 1.3752 (t_1j - 6)+ - 1.6791 (t_1j - 22)+ + 0.6039 (t_1j - 31)+ + 3.4387 t_2j - 1.8527 (t_2j - 4)+ - 3.0626 (t_2j - 17)+ + 1.4184 (t_2j - 23)+ + 4.0628 t_3j - 2.5651 (t_3j - 6)+ - 1.8053 (t_3j - 15)+ + 0.0408 (t_3j - 32)+ + 1.6337 t_4j - 1.8828 (t_4j - 23)+ - 2.2224 (t_4j - 52)+ + 2.2649 (t_4j - 57)+this model have Generalized Cross-Validation (GCV) = 0.0128

Item Type:	Thesis (Masters)
Additional Information:	519.536 Bas e
Uncontrolled Keywords:	Data longitu<;linal, Spline truncated, Regresi nonparametrik, Longitudinal data, Truncated spline, Nonparametric regression.
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 03:58
Last Modified:	01 Oct 2026 03:58
URI:	http://repository.its.ac.id/id/eprint/145132

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