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 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.

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 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 ESTIMASI PARAMETER MODEL REGRESI NONPARAMETRIK B-SPLIN E PADA ANGKA KEMATIAN MATERNAL

2021 ◽  
Vol 10 (3) ◽  
pp. 342
Author(s):  
DHEA ARIESTA ◽  
NURUL GUSRIANI ◽  
KANKAN PARMIKANTI
Keyword(s):  
Cross Validation ◽  
Least Square ◽  
B Spline ◽  
Ordinary Least Square ◽  
Generalized Cross Validation ◽  
Itu Model

Angka kematian maternal menjadi salah satu indikator yang dapat menggambarkan kesejahteraan masyarakat di suatu negara. Pada tahun 2019, di Provinsi Jawa Barat tercatat jumlah kematian ibu sebanyak 684 kasus atau 74,19 per 100.000 kelahiran hidup. Salah satu upaya untuk menurunkan angka kematian maternal di Provinsi Jawa Barat dapat dilakukan dengan memodelkan angka kematian maternal terhadap faktor yang mempengaruhinya sehingga nilai kematian maternal dapat diestimasi. Pada penelitian ini, angka kematian maternal di Provinsi Jawa Barat diestimasi dengan parameter model regresi nonparametrik B-Spline menggunakan pendekatan metode Ordinary Least Square (OLS). Pemilihan regresi nonparametrik B-Spline dikarenakan hasil plotting setiap variabel respon terhadap variabel prediktor tidak menunjukkan pola tertentu, selain itu model regresi B-Spline memiliki fleksibilitas yang tinggi. Model B-Spline terbaik bergantung pada penentuan titik knot optimal yaitu dengan nilai Generalized Cross Validation (GCV) minimum. Setelah dilakukan analisis angka kematian maternal berdasarkan regresi nonparametrik B-Spline diperoleh suatu model terbaik pada saat orde dua dan banyaknya titik knot untuk X1 adalah dua, X2 adalah satu, X3 adalah tiga, dan X4 adalah tiga dengan nilai GCV sebesar 352,3002, sementara nilai koefisien determinasi yang diperoleh sebesar 0, 8443. Kata Kunci: Angka Kematian Maternal, B-Spline, Ordinary Least Square

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.

MODELING OF LOCAL POLYNOMIAL KERNEL NONPARAMETRIC REGRESSION FOR COVID DAILY CASES IN SEMARANG CITY, INDONESIA

2021 ◽  
Vol 14 (2) ◽  
pp. 206-215
Author(s):  
Tiani Wahyu Utami ◽  
Aisyah Lahdji
Keyword(s):  
Nonparametric Regression ◽  
Cross Validation ◽  
Statistical Approach ◽  
Polynomial Kernel ◽  
Model Estimation ◽  
Optimal Bandwidth ◽  
Local Polynomial ◽  
Central Java ◽  
Kernel Approach

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) which was recently discovered. Coronavirus disease is now a pandemic that occurs in many countries in the world, one of which is Indonesia. One of the cities in Indonesia that has found many COVID cases is Semarang city, located in Central Java. Data on cases of COVID patients in Semarang City which are measured daily do not form a certain distribution pattern. We can build a model with a flexible statistical approach without any assumptions that must be used, namely the nonparametric regression. The nonparametric regression in this research using Local Polynomial Kernel approach. Determination of the polynomial order and optimal bandwidth in Local Polynomial Kernel Regression modeling use the GCV (Generalized Cross Validation) method. The data used this research are data on the number of COVID patients daily cases in Semarang, Indonesia. Based on the results of the application of the COVID patient daily cases in Semarang City, the optimal bandwidth value is 0.86 and the polynomial order is 4 with the minimum GCV is 3179.568 so that the model estimation results the MSE is 2922.22 and the determination coefficient is 97%. The estimation results show the highest number of Corona in the Semarang City at the beginning of July 2020. After the corona case increased in July, while the corona case in August decreased.

scholarly journals The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2094
Author(s):  
Ni Putu Ayu Mirah Mariati ◽  
I. Nyoman Budiantara ◽  
Vita Ratnasari
Keyword(s):  
Fourier Series ◽  
Nonparametric Regression ◽  
Simulation Study ◽  
Random Error ◽  
Cross Validation ◽  
Daily Life ◽  
Mixed Data ◽  
Smoothing Spline ◽  
Poor Households ◽  
Mixed Estimator

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

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