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

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 simulati...

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Autores principales:	Ni Putu Ayu Mirah Mariati, I. Nyoman Budiantara, Vita Ratnasari
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	nonparametric regression Smoothing Spline Fourier Series Generalized Cross Validation analysis of variance poor households Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/40e3fb5d89fd4498aa7f681bef977e35
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spelling	oai:doaj.org-article:40e3fb5d89fd4498aa7f681bef977e352021-11-25T19:06:42ZThe Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression10.3390/sym131120942073-8994https://doaj.org/article/40e3fb5d89fd4498aa7f681bef977e352021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2094https://doaj.org/toc/2073-8994In 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.Ni Putu Ayu Mirah MariatiI. Nyoman BudiantaraVita RatnasariMDPI AGarticlenonparametric regressionSmoothing SplineFourier SeriesGeneralized Cross Validationanalysis of variancepoor householdsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2094, p 2094 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonparametric regression Smoothing Spline Fourier Series Generalized Cross Validation analysis of variance poor households Mathematics QA1-939
spellingShingle	nonparametric regression Smoothing Spline Fourier Series Generalized Cross Validation analysis of variance poor households Mathematics QA1-939 Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
description	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.
format	article
author	Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari
author_facet	Ni Putu Ayu Mirah Mariati I. Nyoman Budiantara Vita Ratnasari
author_sort	Ni Putu Ayu Mirah Mariati
title	The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
title_short	The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
title_full	The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
title_fullStr	The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
title_full_unstemmed	The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression
title_sort	application of mixed smoothing spline and fourier series model in nonparametric regression
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/40e3fb5d89fd4498aa7f681bef977e35
work_keys_str_mv	AT niputuayumirahmariati theapplicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression AT inyomanbudiantara theapplicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression AT vitaratnasari theapplicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression AT niputuayumirahmariati applicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression AT inyomanbudiantara applicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression AT vitaratnasari applicationofmixedsmoothingsplineandfourierseriesmodelinnonparametricregression
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The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

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