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

Mariati, Ni Putu Ayu Mirah; Budiantara, I Nyoman; Ratnasari, Vita

doi:10.3390/sym13112094

Cited by 13 publications

(9 citation statements)

References 13 publications

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“…If the time series analysis model does not fulfill stationary properties, then differencing can be performed on the original data to produce data that is closer or stationary. According to [16], the general model of ARIMA (p,d,q) is as follows:…”

Section: Autoregressive Integrated Moving Average (Arima)mentioning

confidence: 99%

Comparison of Local Polynomial Regression and Arima in Predicting the Number of Foreign Tourist Visits to Indonesia

Pratama,

Suryono,

Auliyah

et al. 2024

BAREKENG: J. Math. & App.

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Indonesia is a country that has a variety of exotic tourist destinations and can attract tourists to visit. Currently, tourism is one of the sectors that plays a major role in driving the Indonesian economy. Various tourists, both domestic and foreign, are expected to continue to increase in number every year. Therefore, appropriate policies are needed from the government to develop the tourism sector so that it can be even better over time. This research aims to predict the number of foreign tourist visits to Indonesia using the Autoregressive Integrated Moving Average (ARIMA) model and local polynomial regression. The data used in this research is the number of foreign tourist visits per month from January 2017 to December 2022 obtained from the the Kemenparekraf website. This data is fluctuating so that the method a local polynomial approach is appropriate for this study. The data analysis method used are local polynomial regression and ARIMA model. In the ARIMA model there are assumptions that must be met. In this study, the ARIMA model obtained has met the assumption of residual normality but does not meet the assumption of homoscedasticity so that ARIMA modeling cannot be continued and analysis is only carried out with local polynomial regression. The result of this study is a prediction of future tourist visits. The MAPE value of the local polynomial regression approach is 1.43% which is categorized as a prediction with high accuracy because the value is less than 10%. Thus, the local polynomial regression approach is very well used to predict the number of foreign tourist visits to Indonesia.

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Section: Autoregressive Integrated Moving Average (Arima)mentioning

confidence: 99%

Comparison of Local Polynomial Regression and Arima in Predicting the Number of Foreign Tourist Visits to Indonesia

Pratama,

Suryono,

Auliyah

et al. 2024

BAREKENG: J. Math. & App.

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“…To handle these kinds of data, we should use a mixed estimator, namely, a combination of more than one estimator. Mariati et al [40] discussed a uniresponse multivariable nonparametric regression model using a mixed estimator comprising a smoothing spline and Fourier series that was applied to data of poor households in Bali Province. However, previous researchers, namely, Mariati et al [40], discussed the use of a mixed estimator to estimate a nonparametric regression model, but they only discussed estimating a UNR model in the sense that there is no correlation between the response variables.…”

Section: Introductionmentioning

confidence: 99%

“…Mariati et al [40] discussed a uniresponse multivariable nonparametric regression model using a mixed estimator comprising a smoothing spline and Fourier series that was applied to data of poor households in Bali Province. However, previous researchers, namely, Mariati et al [40], discussed the use of a mixed estimator to estimate a nonparametric regression model, but they only discussed estimating a UNR model in the sense that there is no correlation between the response variables. In this study, therefore, we theoretically discuss a new estimation method using a mixed estimator for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

Chamidah,

Lestari,

Budiantara

et al. 2024

Symmetry

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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties.

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

Cited by 13 publications

References 13 publications

Comparison of Local Polynomial Regression and Arima in Predicting the Number of Foreign Tourist Visits to Indonesia

Comparison of Local Polynomial Regression and Arima in Predicting the Number of Foreign Tourist Visits to Indonesia

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

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

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