Combined estimator Fourier series and spline truncated in multivariable nonparametric regression

Sudiarsa, I Wayan; Budiantara, I Nyoman; Suhartono, Suhartono; Purnami, Santi Wulan

doi:10.12988/ams.2015.55394

Cited by 28 publications

(8 citation statements)

References 22 publications

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“…Previous research that uses mixed estimator have been conducted by (Wayan Sudiarsa et al, 2015), (Nurcahayani et al, 2021), (Nisa' & Budiantara, 2020), which used mixed estimator of truncated spline and Fourier series, and (Mariati et al, 2020) using mixed estimator of smoothing spline and Fourier series. The mixed estimator of kernel and Fourier series has been conducted by (Afifah et al, 2017) and (Nisa et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Estimation of Semiparametric Regression Curve With Mixed Estimator of Multivariable Linear Truncated Spline and Multivariable Kernel

Hesikumalasari¹,

Budiantara

Ratnasari

et al. 2022

Medstat

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The response variable of the regression analysis has a linear relationship with one of the variable predictors, however the unknown relationship pattern with the other predictor variables. Consequently, it can be approached by using semiparametric regression model. The predictor variable that has a linear relationship with the response variable can be approached by using linear parametric curve called parametric component. Meanwhile, the unknown relationship between the response variable with another predictor variable can be approached by using nonparametric curve called nonparametric component. If the predictor variable in nonparametric component is more than one, then it can be approached by using a different nonparametric curve named combined or mixed estimator. In this research, nonparametric component is approached using mixed estimator of multivariable linear truncated spline and multivariable kernel. The objective of this research is to estimate the model of semiparametric regression curve with mixed estimator of multivariable truncated spline and multivariable kernel. Estimation of this mixed model using ordinary least square method.

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Section: Introductionmentioning

confidence: 99%

Estimation of Semiparametric Regression Curve With Mixed Estimator of Multivariable Linear Truncated Spline and Multivariable Kernel

Hesikumalasari¹,

Budiantara

Ratnasari

et al. 2022

Medstat

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“…In addition to the development of research on nonparametric regression, mixed estimators in nonparametric regression have been recently developed. A mixed estimator of the Fourier Series and the Truncated Spline was developed by Sudiarsa et al [8]. The local Polynomial Mixture and Truncated Spline were developed by Suparti et al [9].…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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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“…Considering the concept of semiparametric regression, some studies have proposed combined estimator models to estimate the regression curve, such as spline and kernel functions [21][22][23]. Similarly, in [24], the researchers developed a combined estimator of kernel and Fourier series, whereas in [25][26][27], the researchers presented nonparametric regression with a mixed estimator of truncated spline and Fourier series. Recently, researchers have also been giving attention to a mixed model of longitudinal data, as carried out by [28].…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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.

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Combined estimator Fourier series and spline truncated in multivariable nonparametric regression

Cited by 28 publications

References 22 publications

Estimation of Semiparametric Regression Curve With Mixed Estimator of Multivariable Linear Truncated Spline and Multivariable Kernel

Estimation of Semiparametric Regression Curve With Mixed Estimator of Multivariable Linear Truncated Spline and Multivariable Kernel

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

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

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