Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Rahmawati, Dyah; Budiantara, I Nyoman; Prastyo, Dedy Dwi; Octavanny, Made Ayu Dwi

doi:10.1155/2021/6611084

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…Compared to other regression approaches, non-parametric regression has many advantages. This is because the approach is not limited by the form of a certain function, such as linear, quadratic, or cubic [3].…”

Section: Introductionmentioning

confidence: 99%

ANOVA Decomposition and Importance Variable Process in Multivariate Adaptive Regression Spline Model

Otok¹,

Rumiati²,

Ampulembang³

et al. 2023

Int. J. Adv. Sci. Eng. Inf. Technol.

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This article reviews one of the non-parametric functions, namely the MARS (Multivariate Adaptive Regression Spline) method, a complex combination of recursive partitioning and spline regression. The many advantages of the MARS function over other non-parametric regression functions are of interest to researchers. One of them is it can accommodate the additive and interaction model to improve the prediction and interpretation of the data. There are some important things in the MARS method, namely, ANOVA decomposition and Importance Variable. Decomposition ANOVA is a technique in MARS that is useful for grouping basis function based on variables engagement, whether they enter by one variable or interactions with other variables, making it easier to interpret in graphical form. In comparison, the important variables are a technique that can be used to determine which predictor variables most influence the MARS modeling. This study assesses ANOVA decomposition, and the important variables process in MARS modeling based on GCV and MSE criteria. We use the poverty rate modeling data on Java Island to implement the study results. The results show that the MARS model's interpretation of the poverty rate can be better done through ANOVA decomposition. Besides that, based on GCV and MSE criteria, the result also shows that the biggest variable importance in poverty rate modeling on Java Island is the percentage of per capita expenditure for food, while the smallest is the economic growth variable.

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Section: Introductionmentioning

confidence: 99%

ANOVA Decomposition and Importance Variable Process in Multivariate Adaptive Regression Spline Model

Otok¹,

Rumiati²,

Ampulembang³

et al. 2023

Int. J. Adv. Sci. Eng. Inf. Technol.

View full text Add to dashboard Cite

show abstract

“…There are also non-parametric regression methods in which the form of the model is not clearly defined and their parameters are not taken directly [ 24 , 25 ]. Nonparametric regression methods, including Kernel regression [ 26 , 27 ], LOWESS (locally weighted scatterplot smoothing) [ 22 ], and smoothing spline [ 28 , 29 , 30 , 31 ], have an extensive form of a mathematical model. Nonparametric regression models are much more flexible and computationally complex compared with parametric models.…”

Section: Introductionmentioning

confidence: 99%

Application of Smoothing Spline in Determining the Unmanned Ground Vehicles Route Based on Ultra-Wideband Distance Measurements

Rykała

Typiak

et al. 2022

Sensors

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Unmanned ground vehicles (UGVs) are technically complex machines to operate in difficult or dangerous environmental conditions. In recent years, there has been an increase in research on so called “following vehicles”. The said concept introduces a guide—an object that sets the route the platform should follow. Afterwards, the role of the UGV is to reproduce the mentioned path. The article is based on the field test results of an outdoor localization subsystem using ultra-wideband technology. It focuses on determining the guide’s route using a smoothing spline for constructing a UGV’s path planning subsystem, which is one of the stages for implementing a “follow-me” system. It has been shown that the use of a smoothing spline, due to the implemented mathematical model, allows for recreating the guide’s path in the event of data decay lasting up to a several seconds. The innovation of this article originates from influencing studies on the smoothing parameter of the estimation errors of the guide’s location.

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“…Thus, if it is enforced, it can produce an estimation form that does not match the data pattern [3], [21]. So, it is necessary to develop a mixed estimator of nonparametric regression curves, where each data pattern in the model is approximated by the appropriate curve estimator [1], [3], [4], [20]- [24]. The mixed estimator nonparametric regression model used in this study combines the Truncated Spline and the Gaussian Kernel.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

Ratnasari¹,

Budiantara²,

Dani³

2021

International Journal on Advanced Science, Engineering and Information Technology

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Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R 2 ) value and better accuracy for each combination of sample sizes and variance variations.

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Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Cited by 6 publications

References 27 publications

ANOVA Decomposition and Importance Variable Process in Multivariate Adaptive Regression Spline Model

ANOVA Decomposition and Importance Variable Process in Multivariate Adaptive Regression Spline Model

Application of Smoothing Spline in Determining the Unmanned Ground Vehicles Route Based on Ultra-Wideband Distance Measurements

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

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