Interval Konfidensi Untuk Parameter Model Spline Truncated Regresi Semiparametrik Birespon (Studi Kasus : Data Tingkat Pengangguran Terbuka (TPT) dan Persentase Kemiskinan di Provinsi Jawa Timur)

Ramadhan, Annisa (2020) Interval Konfidensi Untuk Parameter Model Spline Truncated Regresi Semiparametrik Birespon (Studi Kasus : Data Tingkat Pengangguran Terbuka (TPT) dan Persentase Kemiskinan di Provinsi Jawa Timur). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Interval konfidensi dapat digunakan sebagai penentuan pengaruh signifikan variabel prediktor terhadap variabel respon. Penggunaan interval konfidensi dikarenakan nilai pada interval konfidensi tidak terfokus hanya satu titik melainkan pada selang interval atau pada range tertentu. Sehingga interval konfidensi memiliki probabilitas kesalahan lebih kecil dibandingkan menggunakan estimasi titik. Penelitian ini menggunakan interval konfidensi untuk parameter model spline truncated regresi semiparametrik birespon. Penggunaan regresi semiparametrik dikarenakan model memuat komponen parametrik dan kompoen nonparametrik. Keunggulan metode regresi spline truncated yaitu mampu menangani karakteristik data berperilaku berubah-rubah pada sub-sub interval tertentu dan baik dalam penyajian visualnya. Metode yang digunakan dengan pendekatan pivotal quantity dan metode lagrange. Pivotal quantity merupakan metode digunakan untuk mengkonstruksi estimasi interval. Metode lagrange adalah metode untuk mencari nilai maksimum dan minimum suatu fungsi. Penelitian ini diaplikasikan pada data dengan respon Tingkat Pengangguran Terbuka (TPT) dan Persentase Kemiskinan di Jawa Timur. Topik penelitian ini dikarenakan Tingkat Pengangguran Terbuka (TPT) dan persentase kemiskinan di Jawa Timur masih cukup tinggi. Koefisien determinasi yang dihasilkan pada model regresi semiparametrik birespon sebesar 82.09%. Berdasarkan hasil interval konfidensi untuk parameter model didapatkan kesimpulan variabel PDRB dan kepadatan penduduk berpengaruh terhadap variabel TPT persentase kemiskinan.
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Confidence interval can be used as a determination of the significant influence of predictor variables on the response variable. The use of confidence intervals is because the values in the confidence interval are not focused on only one point but at intervals or at a specific range. So that the confidence interval has a smaller probability of error than using point estimation. This study uses confidence intervals for the parameters of the birespon semiparametric regression spline truncated model. The use of semiparametric regression is because the model contains parametric components and nonparametric components. The advantage of the spline truncated regression method is that it is able to handle the data characteristics of changing behavior at certain sub-intervals and good in its visual presentation. The method used is the pivotal quantity approach and the lagrange method. Pivotal quantity is a method used to construct interval estimates. The lagrange method is a method for finding the maximum and minimum values of a function. This study was applied to data with the response to the Open Unemployment Rate (TPT) and the Percentage of Poverty in East Java. The topic of this study is because the Open Unemployment Rate (TPT) and the percentage of poverty in East Java is still quite high. Based on the results of the study, the confidence interval formulation for the birippon spline truncated semiparametric regression model parameters are:   2 1 2 1 2 2 P ( ) ( ) 1 ˆ ˆ ˆ ˆ t t t t t Z Z                 T T H WH H WH H is a parameter matrix, W is a weight matrix variance-covariance y, and 2  ˆ approached with MSE y, ˆ t  m is the estimated parameter of the spline truncated birespon semiparametric regression model. If the resulting confidence interval results in zero, the predictor variable has no significant effect on the model. Estimation of model parameters in TPT and percentage of poverty obtained are:     (1) 1 2 1 1 2 2 ˆ 7.047 10.913 0.084 55.74 35.93 1.781 2.297 1.045 3.282 i i i i i i i y x x t t t t                 (2) 1 2 1 1 2 2 ˆ 0.954 1.026 0.940 0.957 0.051 1.781 0.994 0.015 7.732 i i i i i i i y x x t t t t            The Gini ratio and AHS are estimated to be the symbolic parametric components 1i x and , GRDP and population density are estimated to be symbolic nonparametric components 1i t and 2i t with (1) ˆ i y is the TPT variable and (1) 2 y ˆ is the percentage of poverty. The coefficient of determination generated in the birespon semiparametric regression model was 82.09%. Based on the results of the confidence interval for the model parameters, it is concluded that the GRDP variable and population density influence the TPT variable of the percentage of poverty.

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.536 Ram i-1 2020 3100020085437
Uncontrolled Keywords:	Birespon, Interval Konfidensi, Persentase Kemiskinan, Tingkat Pengangguran, Terbuka, Spline Truncated, Semiparametrik.
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Annisa Ramadhan
Date Deposited:	11 Dec 2025 07:45
Last Modified:	11 Dec 2025 07:45
URI:	http://repository.its.ac.id/id/eprint/74370

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