The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) model

Hidayat, Rahmat; Budiantara, I Nyoman; Otok, Bambang Widjanarko; Ratnasari, Vita

doi:10.1080/03610926.2019.1710201

Cited by 13 publications

(16 citation statements)

References 17 publications

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“…e best model for the biresponse mixed spline smoothing and kernel estimator depends on the optimal smoothing parameters (λ opt ) and optimal bandwidth parameters (α opt ), where λ and α are tuning parameters. ese optimal parameters can be obtained from the model with the smallest generalized cross-validation (GCV) value, see [13][14][15][23][24][25]. e GCV criteria are one of the methods to determine the best model in nonparametric regression [20].…”

Section: Selection Of Smoothing and Bandwidthmentioning

confidence: 99%

“…Although there are often real cases with different patterns between the response and each predictor, if the researcher still insists on applying one type of estimator to all predictor variables, the estimation results can be inaccurate and produce a large error. Researchers have begun to develop nonparametric regression with a mixed estimator, including Hidayat et al [13], Mariati et al [14], and Octavanny et al [15]. ese mixed estimators are formed by referring to the idea of semiparametric regression.…”

Section: Introductionmentioning

confidence: 99%

“…erefore, this study develops a new theory about the mixed estimator of spline smoothing and kernel in biresponse nonparametric regression. is mixed estimator is the development of the mixed estimator proposed by Hidayat et al [13] that the kernel estimator is considered to be fixed, while the kernel function in this paper is estimated. In addition, this new mixed estimator can be applied for biresponse cases.…”

Section: Introductionmentioning

confidence: 99%

“…is method also has the advantage of optimal asymptotic properties over other methods [21,22]. Some researchers develop specific GCV methods according to the model in their research such as the GCV for semiparametric ridge regression with kernel smoothing [23][24][25]; also, several types of GCV were developed for uniresponse nonparametric regression with mixed estimators including the mixed estimator of spline smoothing and kernel [13], mixed estimator of spline smoothing and Fourier series [14], and mixed estimator of truncated spline and fourier series for longitudinal data [15]. erefore, in this study, the determination of the best model was carried out using the GCV method which was developed specifically for the mixed estimator of spline smoothing and kernel in biresponse nonparametric regression.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Rahmawati

Budiantara

Prastyo

et al. 2021

International Journal of Mathematics and Mathematical Sciences

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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.

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Section: Selection Of Smoothing and Bandwidthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Rahmawati

Budiantara

Prastyo

et al. 2021

International Journal of Mathematics and Mathematical Sciences

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“…Besides that Smoothing Spline is able to handle data characters/functions that are smooth. Smoothing Spline also has a very good ability to handle data whose behavior changes at certain sub-intervals [8].…”

Section: Introductionmentioning

confidence: 99%

Smoothing Spline Estimator in Nonparametric Regression (Application: Poverty in Papua Province)

Mariati¹,

Budiantara²,

Ratnasari³

2021

Advances in Social Science, Education and Humanities Research

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Three estimates were obtained in estimating the regression curve, namely estimation of parametric regression, nonparametric regression and semiparametric regression. The most popular nonparametric regression option is smoothing spline. The advantage of smoothing spline is that it can use variable data at certain sub intervals, so this model needs to find its own data estimation. Smoothing Spline allows characters to function smoothly. In everyday life, data patterns are often found to change at certain sub-intervals, one of which is poverty data in Papua Province. Papua Province is ranked first in the percentage of poor people in Indonesia. The best nonparametric Smoothing Spline regression model for the poverty model in Papua Province with a generalized cross validation (GCV) value of 92.77 and R 2 =99.99%.

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The semiparametric regression curve estimation by using mixed truncated spline and fourier series model

Nurcahayani¹,

Budiantara²,

Zain³

2021

International Conference on Mathematics, Computational Sciences and Statistics 2020

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The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) model

Cited by 13 publications

References 17 publications

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Smoothing Spline Estimator in Nonparametric Regression (Application: Poverty in Papua Province)

The semiparametric regression curve estimation by using mixed truncated spline and fourier series model

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