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.

Application of nonparametric regression to groundwater level prediction

1991 ◽  
Vol 18 (4) ◽  
pp. 600-606 ◽  
Author(s):  
Kaz Adamowski ◽  
W. Feluch
Keyword(s):  
Nonparametric Regression ◽  
Groundwater Level ◽  
Cross Validation ◽  
Accurate Prediction ◽  
Nonparametric Model ◽  
Nonparametric Regression Model ◽  
Groundwater Level Fluctuations ◽  
The Relationship ◽  
Sample Experiment ◽  
Validation Stage

A new nonparametric regression model is proposed to investigate the relationship between groundwater level fluctuations and streamflow time series observations. The developed nonparametric model does not force the relationship between variables into a rigidly defined class (i.e., linear regression) and is capable of inferring complicated relationships. The results from the analysis indicate that the nonparametric method gives more accurate prediction results than those obtained from parametric regression. A split-sample experiment shows that nonparametric regression gives accurate prediction (extrapolation) results at the validation stage. Key words: nonparametric regression, cross-validation method, groundwater level, streamflow.

scholarly journals MATRIKS KOVARIANSI DALAM REGRESI NONPARAMETRIK MULTIRESPON PADA KASUS KORELASI SAMA DAN KORELASI TIDAK SAMA

2012 ◽  
Vol 4 (1) ◽  
pp. 161
Author(s):  
Budi Lestari ◽  
I Nyoman Budiantara ◽  
Sony Sunaryo ◽  
Muhammad Mashuri
Keyword(s):  
Regression Model ◽  
Covariance Matrix ◽  
Nonparametric Regression ◽  
Weighted Least Squares ◽  
Multiple Time ◽  
Regression Curve ◽  
Nonparametric Regression Model ◽  
Dependent Variables ◽  
Multiple Time Points ◽  
Jordan Matrix

In the real cases, we are frequently faced the problem in which two or more dependent variables are observed at several values of the independent variables, such as at multiple time points. Multi-response nonparametric regression model, especially smoothing spline model, provides powerful tools to model the function which represents association of among the variables. The  problem is how to estimate nonparametric regression curve of the multi-response nonparametric regression model. The nonparametric regression curve can be estimated  using spline estimator approach, that is by carrying out penalized weighted least-squares optimation. Therefore, we need a covariance matrix which will be used as a weight of the optimation. In this paper, we determine the construction of covariance matrix for both equal and unequal of correlations cases. The results show that the covariance matrices have quite similar construction of diagonal elements but the elements outside the diagonal have very different construction that depend on the construction of the Jordan matrix.

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 Hubungan Faktor Kolestrol Terhadap Gula Darah Diabetes dengan Spline Kubik Terbobot

2020 ◽  
Vol 1 (1) ◽  
pp. 32
Author(s):  
Zhazha Alifkhamulki Ramdhani ◽  
Anna Islamiyati ◽  
Raupong Raupong
Keyword(s):  
Diabetes Mellitus ◽  
Blood Sugar ◽  
Blood Sugar Level ◽  
Cross Validation ◽  
Estimation Method ◽  
Cubic Spline ◽  
Least Square ◽  
Spline Models ◽  
Sugar Levels ◽  
Selection Of

Diabetes Mellitus (DM) is often recognized through an increase in a person's blood sugar level. Factors that can affect the increase in blood sugar levels of DM patients one of which is cholesterol. It usually contains the bookkeeping of several types of cholesterol, including LDL and total cholesterol. DM data are assumed to experience heterokedasticity so that in this study analyzed using regression of weighted cubic spline nonparametric. The estimation method used is weighted least square (WLS). This study aims to obtain a weighted cubic spline model on cholesterol based DM data. The selection of the best model can be seen based on the criteria for the value of generalized cross validation (GCV) minimum. Based on the analysis obtained weighted cubic spline models for cholesterol factors for blood sugar as follows:

scholarly journals Spline and Kernel Mixed Nonparametric Regression for Malnourished Children Model in West Nusa Tenggara

Jurnal Varian ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 99-108
Author(s):  
Muhammad Sopian Sauri ◽  
Mustika Hadijati ◽  
Nurul Fitriyani
Keyword(s):  
Nonparametric Regression ◽  
Mixed Model ◽  
Cross Validation ◽  
Human Life ◽  
Health Sector ◽  
Life Quality ◽  
Regression Curve ◽  
Under Five ◽  
Malnourished Children ◽  
High Degree

Health sector development is essential to improve human life quality, especially in West Nusa Tenggara (NTB) Province. Based on data from the NTB Provincial Health Office from 2011 to 2016, children under five suffering from malnutrition continued to increase, caused by several factors that affected the incident. Therefore, appropriate analysis is needed to model children who suffer from malnutrition in NTB Province in 2016, consisting of 10 districts based on the variables that influence it. The analysis in this study was carried out using a nonparametric regression mixed-model spline truncated and kernel. The estimation of the nonparametric regression curve depends on the optimal knot points and bandwidths parameter. Therefore, in determining the optimal knot points and bandwidths obtained from Generalized Cross-Validation (GCV). Based on the analysis that has been done, we obtained a nonparametric regression mixed-model spline truncated and kernel optimal knot points, such as  for each variable and optimum bandwidths, such as  and , with  the value of GCV. The mixed model acquired has a good model by considering the values of  and MSE. Besides, the MAPE value indicated a high degree of accuracy, so that the model obtained has an excellent forecast.

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 Regresi Spline Polynomial Truncated Biprediktor untuk Identifikasi Perubahan Jumlah Trombosit Pasien Demam Berdarah Dengue

2019 ◽  
Vol 7 (2) ◽  
pp. 97-112
Author(s):  
Anna Islamiyati
Keyword(s):  
Platelet Count ◽  
Longitudinal Study ◽  
Regression Model ◽  
Dengue Fever ◽  
Nonparametric Regression ◽  
Treatment Time ◽  
Model Estimation ◽  
Nonparametric Regression Model ◽  
Simultaneous Model ◽  
Spline Polynomial

Abstract:This paper is a longitudinal study using a nonparametric regression model to identify changes in platelet count from dengue fever. Changes in platelet counts were analyzed based on treatment time and hematocrit count factors. The estimator method proposed is spline polynomial truncated bipredictor. Based on the results of the simultaneous model estimation, we obtained GCV = 714.72 and R2 = 95.9%, it means the model is feasible to explain and identify changes in platelet count based on the time of treatment and the number of hematocrit from DBD patients. Based on the data, there are four patterns of platelet change based on time of treatment and three patterns of platelet change based on hematocrit that are different from each other.Abstrak:Paper ini merupakan studi longitudinal dengan menggunakan model regresi nonparametrik untuk mengidentifikasi perubahan jumlah trombosit demam berdarah. Perubahan jumlah trombosit dianalisis berdasarkan faktor waktu perawatan dan jumlah hematokrit. Metode estimator yang diusulkan adalah spline polynomial truncated bi prediktor. Berdasarkan hasil taksiran model simultan diperoleh GCV = 714,72 dan R2 = 95,9%, artinya model layak untuk menjelaskan dan mengidentifikasi perubahan jumlah trombosit berdasarkan waktu perawatan dan jumlah hematokrit pasien DBD. Berdasarkan data, terdapat empat pola perubahan trombosit berdasarkan waktu perawatan dan tiga pola perubahan trombosit berdasarkan hematokrit yang berbeda satu sama lain.

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%.

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