Pengujian Hipotesis Parameter Komponen Spline Dalam Model Regresi Nonparametrik Campuran Spline dan Kernel

Khusniawati, Faulina (2017) Pengujian Hipotesis Parameter Komponen Spline Dalam Model Regresi Nonparametrik Campuran Spline dan Kernel. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis Regresi adalah sebuah teknik statistik untuk menyelidiki hubungan antara dua variabel atau lebih. Dalam model regresi memungkinkan variabel respon mengikuti kurva regresi nonparametrik karena fungsi regresi tidak diketahui bentuknya. Hubungan variabel respon dengan beberapa variabel prediktor pada regresi nonparametrik tidak selalu menggunakan satu jenis pendekatan seperti spline, kernel, atau deret fourier. Hal ini banyak ditemukan pada regresi nonparametrik antara satu variabel prediktor dengan variabel prediktor lainnya mempunyai pola yang berbeda dengan respon.Pada penelitian ini hubungan antar variabel prediktor dan variabel respon mengikuti model regresi nonparametrik aditif, di mana variabel prediktor didekati dengan fungsi spline truncated dan fungsi kernel. Estimasikurva regresi nonparametrikdiperoleh dariOrdinal Least Square (OLS) dan pemilihan titik knot menggunakan metode Generalized Cross Validation (GCV). Inferensi statistik khususnya pengujian hipotesis untuk kurva regresi dengan pendekatan spline dan kernel dapat dilakukan dengan metode Likelihood RatioTest (LRT). Estimator diperoleh dari membandingkan fungsi likelihood dibawah populasi dan fungsi likelihood di bawah H_0. Selanjutnya pengujian hipotesis yang diperoleh dengan campuran spline dan kernel diaplikasikan pada data Angka Fertilitas Total di Jawa Timur. ====================================================================================== Regression analysis is a statistical technique to model and investigate the relationship between two or more variables. In the regression model allows a response variable follows the curve of the nonparametric regression curves as a function of unknown shape. The correlation of response variables with multiple predictor variables on nonparametric regression does not always use one type approaches such as spline, kernel, or fourier series. It is mostly found in the predictor variables that follow nonparametric regression curves is different between the predictor variable with other predictor variable. Given data pairs in which the correlation between the predictor variables and the response variable follows the additive nonparametric regression model with the predictor variable component approximated by spline function and the truncated kernel function. Estimated nonparametric regression curve was obtained from the Ordinal Least Square (OLS) and point selection knots using Generalized Cross Validation (GCV). Statistical inference particular hypothesis testing for regression curve with spline and kernel approach can be done using Likelihood Ratio Test (LRT). The estimator obtained from comparing the likelihood function under the population and the likelihood function under H0. Further, testing hypothesis obtained with a mixture of spline and kernel applied to the case of fertility in East Java.

Item Type: Thesis (Masters)
Uncontrolled Keywords: Regresi Nonparametrik; Spline; Kernel; Angka Fertilitas Total; Nonparametric Regression; Total Fertility Rate
Subjects: Q Science > QA Mathematics > QA278.2 Regression Analysis
Divisions: Faculty of Mathematics and Science > Statistics > (S2) Master Theses
Depositing User: FAULINA KHUSNIAWATI
Date Deposited: 10 Apr 2017 02:43
Last Modified: 06 Mar 2019 07:01
URI: http://repository.its.ac.id/id/eprint/3070

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