scholarly journals Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dyah P. Rahmawati ◽  
I. N. Budiantara ◽  
Dedy D. Prastyo ◽  
Made A. D. Octavanny
Keyword(s):  
Nonparametric Regression ◽  
Kernel Estimator ◽  
Least Square ◽  
Spline Smoothing ◽  
Nonparametric Regression Model ◽  
Weighted Least Square ◽  
Proposed Model ◽  
Mixed Estimator ◽  
Stage Estimation ◽  
Poor Population

Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

scholarly journals Nonparametric Regression Model for Longitudinal Data with Mixed Truncated Spline and Fourier Series

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Made Ayu Dwi Octavanny ◽  
I. Nyoman Budiantara ◽  
Heri Kuswanto ◽  
Dyah Putri Rahmawati
Keyword(s):  
Fourier Series ◽  
Longitudinal Data ◽  
Nonparametric Regression ◽  
Simulated Data ◽  
Real Data ◽  
Least Square ◽  
Consistent Finding ◽  
Weighted Least Square ◽  
Stage Estimation

Existing literature in nonparametric regression has established a model that only applies one estimator to all predictors. This study is aimed at developing a mixed truncated spline and Fourier series model in nonparametric regression for longitudinal data. The mixed estimator is obtained by solving the two-stage estimation, consisting of a penalized weighted least square (PWLS) and weighted least square (WLS) optimization. To demonstrate the performance of the proposed method, simulation and real data are provided. The results of the simulated data and case study show a consistent finding.

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 Estimasi Fungsi Regresi Dalam Model Regresi Nonparametrik Birespon Menggunakan Estimator Smoothing Spline dan Estimator Kernel

2018 ◽  
Vol 15 (2) ◽  
pp. 20 ◽  
Author(s):  
Budi Lestari
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Kernel Estimator ◽  
Regression Function ◽  
Predictor Variables ◽  
Smoothing Spline ◽  
Estimating Functions ◽  
Nonparametric Regression Model ◽  
Estimation Techniques ◽  
Connection Pattern

Abstract Regression model of bi-respond nonparametric is a regression model which is illustrating of the connection pattern between respond variable and one or more predictor variables, where between first respond and second respond have correlation each other. In this paper, we discuss the estimating functions of regression in regression model of bi-respond nonparametric by using different two estimation techniques, namely, smoothing spline and kernel. This study showed that for using smoothing spline and kernel, the estimator function of regression which has been obtained in observation is a regression linier. In addition, both estimators that are obtained from those two techniques are systematically only different on smoothing matrices. Keywords: kernel estimator, smoothing spline estimator, regression function, bi-respond nonparametric regression model. AbstrakModel regresi nonparametrik birespon adalah suatu model regresi yang menggambarkan pola hubungan antara dua variabel respon dan satu atau beberapa variabel prediktor dimana antara respon pertama dan respon kedua berkorelasi. Dalam makalah ini dibahas estimasi fungsi regresi dalam  model regresi nonparametrik birespon menggunakan dua teknik estimasi yang berbeda, yaitu smoothing spline dan kernel. Hasil studi ini menunjukkan bahwa, baik menggunakan smoothing spline maupun menggunakan kernel, estimator fungsi regresi yang didapatkan merupakan fungsi linier dalam observasi. Selain itu, kedua estimator fungsi regresi yang didapatkan dari kedua teknik estimasi tersebut secara matematis hanya dibedakan oleh matriks penghalusnya.Kata Kunci : Estimator Kernel, Estimator Smoothing Spline, Fungsi Regresi, Model Regresi Nonparametrik Birespon.

Reproducing Kernel Hilbert space and penalized weighted least square in nonparametric regression

2014 ◽  
Vol 8 ◽  
pp. 7289-7300 ◽  
Author(s):  
Adji Achmad Rinaldo Fernandes ◽  
I Nyoman Budiantara ◽  
Bambang Widjanarko Otok ◽  
Suhartono
Keyword(s):  
Hilbert Space ◽  
Nonparametric Regression ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Least Square ◽  
Weighted Least Square

scholarly journals MODEL SPLINE KUBIK DENGAN TITIK-TITIK KNOTS DALAM REGRESI NONPARAMETRIK

2019 ◽  
Author(s):  
Anna Islamiyati
Keyword(s):  
Sobolev Space ◽  
Nonparametric Regression ◽  
Cross Validation ◽  
Optimal Estimation ◽  
Cubic Spline ◽  
Least Square ◽  
Regression Curve ◽  
Estimation Model ◽  
Nonparametric Regression Model ◽  
Spline Polynomial

Let a nonparametric regression model , where is respons variable, is regression curve that assumed an unrestricted form and contained in Sobolev space . For estimate curve is obtained by minimizing the Penalized Least Square (PLS). In this case given cubic spline polynomial approaching for optimal knots points, by using Generalized Cross Validation (GCV) method, to obtained optimal estimation model for regression curve. This application of cubic spline using bread turnover data from CV DEDE MAKASSAR. Based on analysis obtained four optimal knots on the months 3, 6, 8, and 11 by estimation equation as follows : Keywords : PLS, cubic spline, optimal knots, GCV.

scholarly journals Regresi Nonparametrik dengan Pendekatan Deret Fourier pada Data Debit Air Sungai Citarum

2018 ◽  
Vol 4 (2) ◽  
pp. 75-82
Author(s):  
Intaniah Ratna Nur Wisisono ◽  
Ade Irma Nurwahidah ◽  
Yudhie Andriyana
Keyword(s):  
Fourier Series ◽  
Nonparametric Regression ◽  
River Discharge ◽  
Cross Validation ◽  
Least Square ◽  
Nonparametric Regression Model ◽  
Optimal Bandwidth ◽  
Ordinary Least Square ◽  
Calculation Results ◽  
Series Technique

River discharge is one of the factors that affect the occurrence of floods. It varies over time and hence we need to predict the flood risk. Since the plot of the data changes periodically showing a sines and cosines pattern, a nonparametric technique using Fourier series approach may be interesting to be applied. Fourier series can be estimated using OLS (Ordinary Least Square). In a Fourier series, nonparametric regression the level of subtlety of its function is determined by their bandwidth (K). Optimal bandwidth determined using the GCV (Generalized Cross Validation) method. From the calculation results, we have optimal bandwidth which is equal to 16 with R2 is 0.7295 which means that 72.95% of the total variance in the river discharge variable can be explained by the Fourier series nonparametric regression model. Comparing to a classical time series technique, ARIMA Box Jenkins, we obtained ARIMA (1,0,0) with RMSE 83.10 while using Fourier series approach generate a smaller RMSE 50.51.

scholarly journals BIAS COMPARISON NADARAYA WATSON AND LOCALLY LINEAR KERNEL ESTIMATOR OF NONPARAMETRIC REGRESSION

SAINTEKBU ◽  
2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Zulfikar
Keyword(s):  
Nonparametric Regression ◽  
Error Term ◽  
Kernel Estimator ◽  
Least Square ◽  
Finite Variance ◽  
Linear Estimator ◽  
Linear Kernel ◽  
Data Set ◽  
Unknown Form ◽  
Locally Linear

dth: 0px; "> Given a data set (xi , yi ) and connecting between xi and yi be assumed to follownonparametric regression model :yi  m(xi )  i , i  1,2,...,n.Regresssion curve of m be assumed is an unknown form and  i , is an error term in theobservations are IID with mean 0 and finite variance  2.In this paper propose to exist mean conditional estimators with employ the localpolinomial method which polinomial degree p = 0 will be formed the Nadaraya-Watsonestimator and p = 1 to exist the Locally Linear estimator. Furthemore, with the same methodalso be existed the comparison both bias and variance. Kernel estimator will be applied ofthe Canadian Males Data by Murphy and Welch (1990). Key words: Nonparametric estimation, weighted least square, Local polinomial

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