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
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: https://repository.its.ac.id/id/eprint/75423

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