Model Regresi Semiparametrik Campuran Spline Truncated Dan Deret Fourier (Studi Kasus : Angka Harapan Hidup Provinsi Jawa Timur)

Khaerun, Nisa (2017) Model Regresi Semiparametrik Campuran Spline Truncated Dan Deret Fourier (Studi Kasus : Angka Harapan Hidup Provinsi Jawa Timur). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diberikan data berpasangan (x_1i,〖…,x〗_pi,t_1i,…,t_qi,z_1i,…,z_ri,y_i ) hubungan antar variabel prediktor dengan variabel respon mengikuti model regresi semiparametrik campuran
y ̂_i=(x_1i,〖…,x〗_pi,t_1i,…,t_qi,z_1i,…,z_ri )+ε_i
Kurva regresi bersifat aditif, sehingga dapat dituliskan :
μ(x_1i,〖…,x〗_pi,t_1i,…,t_qi,z_1i,…,z_ri )=∑_(j=1)^p▒〖f_j (x_ji )+〗 ∑_(s=1)^q▒〖g_s (g_si )+〗 ∑_(l=1)^r▒〖h_l (z_li ) 〗
Komponen kurva regresi f_j (x_ji ) didekati dengan fungsi parametrik linier, komponen kurva regresi g_s (g_si ) didekati dengan fungsi Spline Truncated dan komponen kurva regresi h_l (z_li ) didekati dengan fungsi Deret Fourier. Tujuan dari penelitian ini adalah memperoleh bentuk estimator dalam regresi semiparametrik dengan menggunakan estimator campuran Spline Truncated dan Deret Fourier menggunakan metode Penalized Least Square (PLS), serta memodelkan Angka Harapan Hidup di Provinsi Jawa Timur menggunakan model regresi semiparametrik campuran tersebut. Hasil kajian menghasilkan bahwa estimator kurva regresi parametrik linier f ̃ ̂(x)=A(K,λ,k) Y ̃ estimator kurva regresi Spline Truncated g ̃ ̂(t)=B(K,λ,k) Y ̃ dan kurva regresi Deret Fourierh ̃ ̂(z)=C(K,λ,k) Y ̃. Selanjutnya, diperoleh estimasi model regresi semiparametrik campuran Spline Truncated dan Deret Fourier adalah
y ̂_i=μ ̂(x_1i,〖…,x〗_pi,t_1i,…,t_qi,z_1i,…,z_ri )=f ̂(x)+g ̃ ̂(t)+h ̃ ̂(z)=F(K,λ,k) Y ̃
dengan F(K,λ,k)=A(K,λ,k)+B(K,λ,k)+C(K,λ,k). Model regresi semiparametrik campuran ini bergantung pada lokasi titik-titik knot K, parameter penghalus lambda dan osilasi k. Model regres semiparametrik campuran Spline Truncated dan Deret Fourier terbaik diperoleh dengan cara meminimumkan fungsi Generalized Cross Validation. Model regresi semiparametrik campuran yang diperoleh digunakan untuk memodelkan data kasus Angka Harapan Hidup (AHH) di Provinsi Jawa Timur. Model estimator campuran tersebut menghasilkan R2 sebesar 99,62%.

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Given the data pairs
1 2 1 2 1 2 ( , , , , , , , , , , , , ). i i pi i i qi i i ri i x x x t t t z z z y
The relationship
between predictor variables with response variable following semiparametric
regression model
  1 1 1 , , , , , , , , . i i pi i qi i ri i y x x t t z z    
The Regression curves are additive, so it can be written :
 1 1 1 
1 1 1
, , , , , , , , ( ) ( ) ( ).
p q r
i pi i qi i ri j ji s si l li
j s l
 x x t t z z f x g t h z
  
     
Component of regression curve
( ) j ji f x
approached by a linear parametric
function, component regression curve
( ) s si g t
approached by Spline Truncated
function and component regression curve
( ) l li h z
approached by Fourier Series
function. The purpose of this research are to obtained the estimator of
semiparametric regression model with combined estimator of Spline Truncated
and Fourier Series using Penalized Least Square method (PLS), and modeling the
case of life expectancy in Province of East Java using mixture semiparametric
regression model. The results show that the estimator of parametric linier
regression curve
ˆ
f x K k Y ( ) ( , , ) ,  A 
the estimator of Spline Truncated
ˆ
g t K k Y ( ) ( , , )  B 
and the estimator of Fourier Series is
ˆ
h z K k Y ( ) ( , , ) .  C 
Furthermore, the mix estimator of Spline Truncated and Fourier Series in
semiparametric regression model is
  1 1 1
ˆ ˆ
ˆ
ˆ ˆ , , , , , , , , ( ) ( ) ( ) ( , , ) , i i pi i qi i ri y x x t t z z f x g t h z k K Y        F
with
F A B C ( , , ) ( , , ) ( , , ) ( , , ). K k K k K k K k       
This mixture semiparametric
regression model depends on the location of the dots knots , smoothing parameter
lambda and oscillation. The best model of semiparametric regression model with
combined estimator of Spline Truncated and Fourier series can be obtained by
minimizing the function of Generalized Cross Validation. The mixture estimator
model produces R2
of 99,62%.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Regresi Semiparametrik; Estimator Campuran; Spline Truncated; Deret Fourier; PLS; Semiparametric Regression; Fourier Series; Combined Estimator
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	- KHAERUN NISA
Date Deposited:	08 Mar 2017 01:37
Last Modified:	06 Mar 2019 04:13
URI:	http://repository.its.ac.id/id/eprint/2744

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