Pemodelan Regresi Semiparametrik Menggunakan Estimator Campuran Spline Truncated Dan Kernel

., Hesikumalasari (2016) Pemodelan Regresi Semiparametrik Menggunakan Estimator Campuran Spline Truncated Dan Kernel. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Variabel respon pada analisis regresi dapat memiliki hubungan linear dengan
salah satu variabel prediktor, namun dengan variabel prediktor yang lain tidak
diketahui bentuk pola hubungannya. Pola data seperti ini dapat dimodelkan
dengan model regresi semiparametrik. Diberikan data berpasangan
( , , , ) i i i i x t z y
dan diasumsikan hubungan antar variabel prediktor dengan variabel respon
mengikuti model regresi semiparametrik
( , , ) i i i i i y x t z     . Kurva
( , , ) i i i  x t z
dapat ditulis dalam bentuk
( , , ) ( ) ( ) ( ) i i i i i i  x t z f x g t h z    . Kurva regresi
( )i
f x
dihampiri dengan parametrik linear,
g( )i
t
dihampiri dengan fungsi
nonparametrik spline truncated dan
( ) h zi
dihampiri dengan fungsi
nonparametrik kernel. Tujuan dari penelitian ini adalah memperoleh bentuk
estimator dalam regresi semiparametrik dengan menggunakan estimator
campuran spline truncated dan kernel. Berdasarkan hasil kajian diperoleh
estimator kurva regresi parametrik linear adalah
ˆ
f x k y ( ) ( , )  C 
, estimator
kurva regresi spline truncated adalah
ˆ
g t k y ( ) ( , )  K 
dan estimator kurva
regresi kernel adalah
ˆ
h z y ( ) ( ))  D 
. Selanjutnya diperoleh estimator kurva
regresi semiparametrik campuran spline truncated dan kernel
ˆ
  ( , , ) ( , ) x t z k y  M
, dengan
M C K D ( , ) ( , ) ( , ) ( ) k k k        . Estimator
campuran ini tergantung pada titik knot dan parameter bandwith. Estimator
terbaik diperoleh dengan cara meminimumkan fungsi Generalized Cross
Validation. Model yang diperoleh kemudian diterapkan pada data produksi padi
di Jawa Tengah. Model yang diperoleh adalah model estimator campuran yang
menghasilkan R2
sebesar 91,91%.
=====================================================================================================
The response variable of the regression analysis has a linear relationship with
one of the variable predictors inspite of the unknown relationship pattern with
the other variables. Consequently, it can be approached by using
semiparametric regression model. As given pair data
( , , , ) i i i i x t z y
and assumed
the relationship between predictor variable and response variable are
approached by using semiparametric regression ( , , ) i i i i i y x t z     , Combined
curve
( , , ) i i i  x t z
can be written as
( , ) ( ) ( ) ( ) i i i i i  x t f x g t h z   
. Regression
curve
( )i
f x
is investigated by using parametric linear, regression curve
g( )i
t
is
investigated by using truncated spline function and
( ) h zi
is approached by
using kernel function. The objective of this research is to obtain the pattern of
combined estimator in semiparametric regression by using the estimator of a
combination of truncated spline and kernel. Based on result obtained the
estimator of linear parametric curve is
ˆ
f x k y ( ) ( , )  C 
, the estimator of spline
truncated curve is
ˆ
g t k y ( ) ( , )  K 
, and the estimator of kernel curve is
ˆ
h z y ( ) ( ))  D 
. Then the estimator of combined of spline truncated and kernel
semiparametric curve is
ˆ
  ( , , ) ( , ) x t z k y  M
, where
M C K D ( , ) ( , ) ( , ) ( ) k k k        . The estimator of this combination depends
on knot points and badwith parameter. Best estimator are resulted by
minimizing the Generalized Cross Validation function. The combination of
truncated spline and kernel for Semiparametric regression model which have
been obtained will be applied on East Java’s rice production data. Model that
obtained is combined estimator model with R2
is 91.91%.

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.536 Hes p 3100016066243
Uncontrolled Keywords:	Regresi Semiparametrik, Spline Truncated, Kernel, Estimator Campuran, Semiparametric Regression, Spline Truncated, Kernel, Combine 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:	- Davi Wah
Date Deposited:	19 Mar 2020 22:46
Last Modified:	19 Mar 2020 22:46
URI:	http://repository.its.ac.id/id/eprint/75423

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