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.  

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 Analyzing The Effect of BI 7-Days Repo Rate on The Jakarta Composite Index Using Nonparametric Regression Approaches Based on Least Square Spline Estimator

2021 ◽  
Vol 17 (3) ◽  
pp. 447-461
Author(s):  
Christopher Andreas ◽  
Feevrinna Yohannes Harianto ◽  
Elfhira Juli Safitri ◽  
Nur Chamidah
Keyword(s):  
Nonparametric Regression ◽  
Composite Index ◽  
Negative Relationship ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Percentage Error ◽  
Absolute Deviation ◽  
Parametric Regression ◽  
Regression Approach ◽  
Repo Rate

During the Covid-19 pandemic, the Indonesia stock market was under great pressure, so that the value of the Jakarta Composite Index (JCI) fluctuated greatly. To maintain economic stability, Bank Indonesia has regulated monetary policy such as setting the BI 7-Days Repo Rate. Analysis of this effect is important to formulate the right policy. This study aims to design the best model in describing the relationship between JCI value and BI 7-Days Repo Rate. The analysis was carried out by using parametric regression approach based on the ordinary least square method and nonparametric regression approach based on least square spline estimator. The results showed that the parametric regression models failed to meet the classical assumptions. Meanwhile, nonparametric regression can produce an optimal model with high accurate prediction, with an overall mean absolute percentage error value of 3.16%. Furthermore, mean square error, coefficient of determination, and mean absolute deviation also show good results. Thus, the effect of the BI 7-Days Repo Rate on the JCI value forms a quadratic pattern, in which a positive relationship is formed when the BI 7-Days Repo Rate is set at more than 4.25% and vice versa for a negative relationship.

scholarly journals PENGUJIAN HIPOTESIS SIMULTAN MODEL REGRESI NONPARAMETRIK SPLINE TRUNCATED DALAM PEMODELAN KASUS EKONOMI

2020 ◽  
Vol 1 (2) ◽  
pp. 98-106
Author(s):  
ANDREA TRI RIAN DANI ◽  
NARITA YURI ADRIANINGSIH ◽  
ALIFTA AINURROCHMAH
Keyword(s):  
Nonparametric Regression ◽  
Predictor Variable ◽  
Coefficient Of Determination ◽  
Poor People ◽  
Nonparametric Regression Model ◽  
Response Variable ◽  
Simultaneous Testing ◽  
Regression Approach ◽  
Best Estimator

The pattern in a relationship between the response variable and the predictor variable can be known and some cannot be known. In determining the unknown pattern of relationships, nonparametric regression approaches can be used. The nonparametric regression approach is very flexible. One of the most frequently used nonparametric regression approaches is the truncated spline. Truncated splines are polynomial pieces that are segmented and continuous. The purpose of this study is to obtain the best estimator model in the Gini Ratio case against the variables suspected of influencing it, then perform simultaneous hypothesis testing on the nonparametric regression model. The criteria for the goodness of the model use the GCV and R2 values. In the case modeling of the District / City Gini Ratio in East Java Province using a nonparametric regression approach, it was found that the truncated spline estimator with 3 knots points gave quite good results. This is indicated by the coefficient of determination of the truncated spline estimator, which is 84.76%. Based on the results of simultaneous testing, it was found that the open unemployment rate, the percentage of poor people and the rate of economic growth simultaneously had an influence on the Gini Ratio.

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 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

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