Septiningrum, Lutfia (2020) Estimator Matriks Variance-Covariance Spline Truncated Pada Regresi Nonparametrik Birespon. Masters thesis, Intitut Teknologi Sepuluh Nopember.
Preview |
Text
06211850010006-Master_Thesis.pdf Download (3MB) | Preview |
Abstract
Regresi nonparametrik birespon berbeda dengan regresi nonparametrik respon tunggal, dimana model birespon terdiri dari dua variabel respon dengan asumsi terdapat korelasi antar respon. Untuk mengakomodir korelasi antar respon, maka estimasi fungsi regresi memuat matriks bobot berupa matriks variance covariance error. Berdasarkan penelitian sebelumnya, matriks variance covariance diasumsikan sebagai fixed value. Sedangkan dalam kasus riil tidak diketahui nilainya, maka matriks variance covariance tersebut harus diestimasi dari data. Sehingga, tujuan penelitian ini adalah mengestimasi matriks variance covariance untuk mendapatkan model regresi nonparametrik birespon menggunakan spline truncated. Terdapat dua tahap untuk mengestimasi matriks variance covariance. Tahap pertama adalah melakukan estimasi terhadap koefisien regresi nonparametrik birespon menggunakan metode Weighted Least Square (WLS). Tahap kedua adalah mengestimasi matriks variance covariance menggunakan metode MLE dengan mengasumsikan error berdistribusi normal bivariat dengan mean 0 dan variance covariance W. Selanjutnya dilakukan penerapan terhadap data riil yaitu pada data Indeks Pembangunan Manusia (IPM) dan Indeks Pembangunan Gender (IPG). Variabel prediktor yang digunakan adalah angka kesakitan, angka partisipasi kasar SMA dan PDRB Perkapita. Kriteria pemilihan model terbaik berdasarkan titik knot optimum menggunakan nilai Generalized Cross Validation (GCV). Diperoleh model terbaik pada satu titik knot spline linier dengan GCV 14,183. Model hasil estimasi parameter menggunakan matriks variance covariance lebih baik dalam memodelkan data IPM dan IPG Kabupaten/Kota di Pulau Jawa karena mempunyai RMSE sebesar 3,597 lebih kecil dibandingkan model hasil estimasi parameter dengan matriks variance covariance diketahui mempunyai RMSE sebesar 5,019.
===============================================================================================================================
Bi-response nonparametric regression is different from uniresponse nonparametric regression, where bi-response model consists of two response variables with the assumption of dependency. To accommodate the correlation between responses, the estimation of regression function should be consisted of weight in the form of variance covariance matrix of residuals. It can be estimated using variance covariance error matrix. Based on previous research, the variance covariance matrix is assumed to be a fixed value. Whereas in the real case the value is unknown so that the variance covariance matrix must be estimated from the data. The purpose of this study is to estimate the variance covariance matrix of spline truncated on bi-response nonparametric regression models. There are two steps to estimate the variance covariance matrix. The first step is to estimate the Bi-response nonparametric regression coefficient using the Weighted Least Square (WLS) method and the second step is estimated the variance covariance matrix using the MLE method by assuming a bivariate normal distribution error with mean 0 and variance covariance W. Then, the result of the estimation is applied to the Human Development Index (HDI) and Gender Development Index (IPG) data. The predictor variables used were morbidity, gross participation rates of SMA and GDP per capita. Criteria for selecting the best model based on the optimum knot point uses the Generalized Cross Validation (GCV) value. The best model found was spline truncated use one knot with GCV 14.183. The estimation parameter model by using the variance covariance matrix is fit in modeling the HDI and GDI data since the RMSE is smaller than that of fixed variance covariance matrix.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.536 Sep e-1 2020 |
| Uncontrolled Keywords: | Birespon, GCV, IPG, IPM, Matriks Variance-Covariance |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Lutfia Septiningrum |
| Date Deposited: | 09 May 2023 06:59 |
| Last Modified: | 09 May 2023 06:59 |
| URI: | http://repository.its.ac.id/id/eprint/73860 |
Actions (login required)
 |
View Item |