Semiparametric regression based on three forms of trigonometric function in fourier series estimator

Mardianto, M. Fariz Fadillah; Tjahjono, Eko; Rifada, Marisa

doi:10.1088/1742-6596/1277/1/012052

Cited by 4 publications

(5 citation statements)

References 9 publications

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“…The Fourier series is a curve that shows the sine and cosine functions. By expansion into the form of a Fourier series, a periodic function can be expressed as the sum of several harmonic functions, namely functions of sine and cosine, including sinusoidal functions [17]:…”

Section: A Biresponse Nonparametric Regressionmentioning

confidence: 99%

Comparison of Salinity and Seawater Temperature Predictions Using Var and Biresponse Fourier Series Estimator

Faisol

Ukhrowi

Mardianto

et al. 2022

BAREKENG: J. Math. & App.

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Salinity is the concentration of dissolved salts in water. The salt in question is a variety of ions dissolved in water, including table salt (NaCl). Salinity and seawater temperature are one of the factors that affect salt production. The higher the NaCl content, the better the quality of the salt. Currently, people's salt production is still unable to meet the needs of national salt, especially industrial salt, because most of the quality of people's salt still does not meet the SNI criteria for industrial salt. Thus, it is necessary to predict the salinity and temperature of seawater to help determine the next steps or policies in improving the quality of people's salt. Predictions of salinity and seawater temperature were carried out by applying the Vector Autoregressive (VAR) Analysis method and nonparametric Fourier series regression with primary data of salinity and seawater temperature on the coast of Tlesah Tlanakan Beach, Pamekasan. The best model chosen is the model that has the smallest error size and the highest accuracy measure. The best models are nonparametric regression of the Fourier series of sine and cosine bases with the predicted result obtaining a MAPE value is 0.00496 and coefficient of determination is 100%.

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Section: A Biresponse Nonparametric Regressionmentioning

confidence: 99%

Comparison of Salinity and Seawater Temperature Predictions Using Var and Biresponse Fourier Series Estimator

Faisol

Ukhrowi

Mardianto

et al. 2022

BAREKENG: J. Math. & App.

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“…Determination of optimal λ can use Generalized Cross Validation (GCV) method. Based on [15,16], formula of GCV can be written as follows:…”

Section: Selection Of Oscillation Parametersmentioning

confidence: 99%

“…The best model that can be used for prediction needs to pass the goodness of criteria. The goodness of criteria is the smallest GCV value for an optimal oscillation parameter, the smallest MSE value, and the enormous determination coefficient value [15,16].…”

Section: Selection Of Oscillation Parametersmentioning

confidence: 99%

Contribution Analysis of “Suroboyo Bus” in Waste Management Based on Two Form of Complete Fourier Series Estimator

et al. 2021

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Plastic waste is a problem that almost exists in all countries. This problem arises because of the lack of facilities that can handle the plastic waste. Suroboyo Bus is an innovation for this problem because Suroboyo Bus uses plastic bottles as payment. The purpose of this research is to predict the percentage contribution of Suroboyo Bus in handling plastic waste. The Fourier series estimator performs well for data modeling with seasonal trend patterns. This paper examines two approaches to the Fourier series. The difference between the approaches is the inclusion of the phi (π) function in the model. The result shows the goodness of fit criterion model with π function are for and 0,08% for MAPE whereas the fit criterion model without π function is 100% for and 0,07% for MAPE. In conclusion, the Fourier series model without the π function is better because the Fourier series model without the π function is more satisfy the goodness of fit criteria than the Fourier series model with the π.

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“…iii. Estimators for semiparametric regression curves in vector equations are as follows ˆŷ = Xβ + Tη (11) Proof Parameter estimation in the Fourier series semiparametric regression model for longitudinal data obtained by optimization of Weighted Least Square (WLS) is done to minimize the goodness of fit of the semiparametric regression model with the Fourier series approach for longitudinal data y -f(x, t) y -f(x, t) (12) by elaborating on equation 12, WLS optimization from is given as fallows :…”

Section: The Fourier Estimator In Semiparametric Regression For Lmentioning

confidence: 99%

“…Moreover, the advantage of the Fourier series is that it is able to overcome the data patterns that have oscillation pattern [9]. Research about Fourier series estimators [5], [10], [11], [12]. All of recent study is about cross section data.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Study of Fourier Series Estimator in Semiparametric Regression for Longitudinal Data Based on Weighted Least Square Optimization

Kuzairi¹,

Chamidah²,

Budiantara³

2020

Proceedings of the 1st International Multidisciplinary Conference on Education, Technology, and Engineering (IMCETE 2019)

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Semiparametric regression approach is a combination of two components, namely the parametric regression component and the nonparametric regression component. The data used in this study is longitudinal data. Longitudinal data is data obtained from repeated observations of each subject at different time intervals. This data correlates to the same subject and is independent between different subjects. In this study the parametric component is assumed to be linear and the nonparametric component is approximated by the Fourier Series function. In this study, we determine the estimator for semiparametric regression parameters longitudinal data using Weighted Least Square (WLS). In the semiparametric regression based on Fourier series estimator for longitudinal data, the optimal oscillation parameter k will be selected. To get the estimation of model parameters, the WLS optimization is performed and GCV method is used to determine the optimal k. After obtaining the optimal oscillation parameters from the minimum GCV, the oscillation parameters are used again in the Fourier series semiparametric regression modeling. The criteria for goodness of the model use and the value of MSE. The best model is a model that has a high value and a small MSE value.

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Semiparametric regression based on three forms of trigonometric function in fourier series estimator

Cited by 4 publications

References 9 publications

Comparison of Salinity and Seawater Temperature Predictions Using Var and Biresponse Fourier Series Estimator

Comparison of Salinity and Seawater Temperature Predictions Using Var and Biresponse Fourier Series Estimator

Contribution Analysis of “Suroboyo Bus” in Waste Management Based on Two Form of Complete Fourier Series Estimator

Theoretical Study of Fourier Series Estimator in Semiparametric Regression for Longitudinal Data Based on Weighted Least Square Optimization

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