The semiparametric regression curve estimation by using mixed truncated spline and fourier series model

2021 ◽  
Author(s):  
Helida Nurcahayani ◽  
I. Nyoman Budiantara ◽  
Ismaini Zain
Keyword(s):  
Fourier Series ◽  
Semiparametric Regression ◽  
Regression Curve ◽  
Curve Estimation

scholarly journals Estimation of Heteroskedasticity Semiparametric Regression Curve Using Fourier Series Approach

2020 ◽  
Vol 2 (1) ◽  
pp. 14-20
Author(s):  
Rahmawati Pane ◽  
Sutarman
Keyword(s):  
Fourier Series ◽  
Regression Model ◽  
Variable Parameter ◽  
Predictor Variable ◽  
Semiparametric Regression ◽  
Least Square ◽  
Parameter Vector ◽  
Regression Curve ◽  
Semiparametric Regression Model ◽  
Main Components

A heteroskedastic semiparametric regression model consists of two main components, i.e. parametric component and nonparametric component. The model assumes that any data (x̰ i′ , t i , y i ) follows y i = x̰ i′ β̰+ f(t i ) + σ i ε i , where i = 1,2, … , n , x̰ i′ = (1, x i1 , x i2 , … , x ir ) and t i is the predictor variable. Parameter vector β̰ = (β 1 , β 2 , … , β r ) ′ ∈ ℜ r is unknown and f(t i ) is also unknown and is assumed to be in interval of C[0,π] . Random error ε i is independent on zero mean and varianceσ 2 . Estimation of the heteroskedastic semiparametric regression model was conducted to evaluate the parametric and nonparametric components. The nonparametric component f(t i ) regression was approximated by Fourier series F(t) = bt + 12 α 0 + ∑ α k 𝑐 𝑜𝑠 kt Kk=1 . The estimation was obtained by means of Weighted Penalized Least Square (WPLS): min f∈C(0,π) {n −1 (y̰− Xβ̰−f̰) ′ W −1 (y̰− Xβ̰− f̰) + λ ∫ 2π [f ′′ (t)] 2 dt π0 } . The WPLS solution provided nonparametric component f̰̂ λ (t) = M(λ)y̰ ∗ for a matrix M(λ) and parametric component β̰̂ = [X ′ T(λ)X] −1 X ′ T(λ)y̰

scholarly journals ESTIMASI MODEL REGRESI SEMIPARAMETRIK MENGGUNAKAN ESTIMATOR KERNEL UNIFORM (Studi Kasus: Pasien DBD di RS Puri Raharja)

2015 ◽  
Vol 4 (4) ◽  
pp. 176
Author(s):  
ANNA FITRIANI ◽  
I GUSTI AYU MADE SRINADI ◽  
MADE SUSILAWATI
Keyword(s):  
Body Temperature ◽  
Regression Model ◽  
Linear Regression Analysis ◽  
Kernel Estimator ◽  
Semiparametric Regression ◽  
Regression Function ◽  
Multiple Linear Regression Analysis ◽  
Regression Curve ◽  
Optimal Bandwidth ◽  
Curve Estimation

Semiparametric regression model estimation is an estimation that combines both parametric and nonparametric regression model. In semiparametric regression, some of the variables are parametrics and the others are nonparametrics. Semiparametric regression is used when relationship pattern between independent and depentdent variables is half known  and half unknown. Regression curve smoothing technique in nonparametric components in this study was using uniform kernel function. The optimal semiparametric regression curve estimation was obtained by optimal bandwidth. By choosing optimal bandwidth, we would obtain a smooth regression curve estimation in respect to data pattern. In choosing optimal bandwidth, we use minimum GCV as a criteria.The purpose of this study was to estimate the semiparametric regression function of dengue fever case using uniform kernel estimator. There were 6 independent variables namely age (in years) body temperature (in Celcius), heartbeat (in times/minutes) hematocryte ratio (in percent), amount of trombocyte (× 103/ul) and fever duration ( in days). Age, body temperature, heartbeat, amount of trombosyte and fever duration are parametric components and hematocryte ration is a nonparametric component. The optimal bandwidth (h) which was obtained with minimum GCVwas 0,005. The value of MSE which was obtained by using multiple linear regression analysis was 0,031 and by using semiparametric regression was 0,00437119.

scholarly journals Estimation Curve Semiparametric Regression with the Spline Linear Approach to Poverty Data in Bali Province

2021 ◽  
pp. 96-107
Author(s):  
I Wayan Sudiarsa
Keyword(s):  
Economic Growth ◽  
Semiparametric Regression ◽  
Least Square ◽  
Poor People ◽  
Optimization Approach ◽  
Regression Curve ◽  
Curve Estimation ◽  
Ordinary Least Square ◽  
Linear Approach ◽  
The One

In semiparametric regression, nonparametric components can be approached by spline. Splines are pieces of polynomial that are segmented and continuous. The one advantages of spline is the presence of knot points that indicate changes in the pattern of data behavior. This research purposetoobtain semiparametric regression curve estimation with linear spline approach. The method of optimization approach used by ordinary least square (OLS). Based on this research, there are two variables that have a significant effect on the percentage of poor people in Bali Province, namely the Open Unemployment the rate of economic growth. The total variance of response that can be explained by predictor in this model is 67.97% with MSE of 9.7854.  

scholarly journals The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1141
Author(s):  
Helida Nurcahayani ◽  
I Nyoman Budiantara ◽  
Ismaini Zain
Keyword(s):  
Fourier Series ◽  
Nonparametric Regression ◽  
Estimation Method ◽  
Size Variation ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Regression Curve ◽  
Curve Estimation ◽  
Weighted Least Square ◽  
Proposed Model

Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

scholarly journals Estimator Deret Fourier Dalam Regresi Nonparametrik dengan Pembobot Untuk Perencanaan Penjualan Camilan Khas Madura

2018 ◽  
Vol 4 (1) ◽  
pp. 18-23
Author(s):  
Anisatus Sholiha ◽  
Kuzairi Kuzairi ◽  
M. Fariz Fadillah Madianto
Keyword(s):  
Fourier Series ◽  
Nonparametric Regression ◽  
Semiparametric Regression ◽  
Least Square ◽  
Predictor Variables ◽  
Regression Curve ◽  
Parametric Regression ◽  
Determination Coefficient ◽  
Regression Estimators ◽  
The Relationship

The purpose of regression analysis is determining the relationship between response variables to predictor variables. To estimate the regression curve there are three approaches, parametric regression, nonparametric regression, and semiparametric regression. In this study, the estimator form of nonparametric regression curve is analyzed by using the Fourier series approach with sine and cosine bases, sine bases, and cosine bases. Based on Weighted Least Square (WLS) optimization, the estimator result can be applied to model the sale planning of Madura typical snacks. Nonparametric regression estimators with the Fourier series approach are weighted with uniform and variance weight. The best model that be obtained in this study for uniform weight, based on cosine and sine basis with GCV value ​​of 1541.015, MSE value of 0.1375912 and determination coefficient value of 0.4728418%. The best model for variance weight is based on cosine and sine basis with a GCV value of 1541.011, MSE value of 0.1375912 and determination coefficient of 0.4728227%.

scholarly journals Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

2017 ◽  
Vol 855 ◽  
pp. 012002 ◽  
Author(s):  
Ngizatul Afifah ◽  
I Nyoman Budiantara ◽  
I Nyoman Latra
Keyword(s):  
Fourier Series ◽  
Semiparametric Regression ◽  
Mixed Estimator

Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province

2021 ◽  
pp. 69-82
Author(s):  
Ni Putu Ayu Mirah Mariati ◽  
Nyoman Budiantara ◽  
Vita Ratnasari
Keyword(s):  
Nonparametric Regression ◽  
Semiparametric Regression ◽  
Poor People ◽  
Regression Curve ◽  
Parametric Regression ◽  
Regression Approach ◽  
Spline Estimation ◽  
High Flexibility

In estimating the regression curve there are three approaches, namely parametric regression, nonparametric regression and semiparametric regression. Nonparametric regression approach has high flexibility. Nonparametric regression approach that is quite popular is Truncated Spline. Truncated Spline is a polynomial pieces which have segmented and continuous. One of the advantages of Spline is that it can handle data that changes at certain sub intervals, so this model tends to search for data estimates wherever the data pattern moves and there are points of knots. In reality, data patterns often change at certain sub intervals, one of which is data on poverty in the Papua Province. Papua Province is ranked first in the percentage of poor people in Indonesia. The best of model Truncated Spline in nonparametric regression for the poverty model in Papua Province is using a combination of knot.  

The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) model

2020 ◽  
pp. 1-12 ◽  
Author(s):  
Rahmat Hidayat ◽  
I. Nyoman Budiantara ◽  
Bambang W. Otok ◽  
Vita Ratnasari
Keyword(s):  
Smoothing Spline ◽  
Regression Curve ◽  
Curve Estimation
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