Spline Estimator in Homoscedastic Multi-Response Nonparametric Regression Model in Case of Unbalanced Number of Observations

Chamidah, Nur; Lestari, Budi

doi:10.17654/ms100091433

Cited by 25 publications

(9 citation statements)

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“…The Fourier series in equation (2) only accommodate seasonal pattern. For accommodating trend and seasonal pattern, [5], appended and modified equation (2) with linear function as follows:…”

Section: The Fourier Estimator In Semiparametric Regression For Lmentioning

confidence: 99%

“…In regression analysis the relationship pattern between the response variable and the predictor variable, is not always parametric patterned such as linear, quadratic, cubic and others. There are several cases where the pattern of relationships between response variables and predictor variables have uncertain pattern, it can be solving with nonparametric regression such as spline [2], local polynomial [1], local linear [3], kernel [4], and Fourier series [5]. Evenly, in some other cases, there are some pattern that have uncertain pattern, and the others have certain pattern like linear.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Fourier Estimator In Semiparametric Regression For Lmentioning

confidence: 99%

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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“…Estimator spline yang diperoleh dengan menggunakan metode least square disebut least square Spline. Peneliti yang menggunakan estimator spline dalam regresi nonparametrik antara lain Lestari et al [4], Islamiyati, et al [5] and Ayidin and Yilmaz [6].…”

Section: Pendahuluanunclassified

Analisis Pengaruh Angka Kematian Bayi Terhadap Angka Harapan Hidup Di Provinsi Jawa Timur Berdasarkan Estimator Least Square Spine

Novia

Tegarina

et al. 2019

Contemp. Math. App

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Life expectancy can be used to evaluate the government's performance for improving the welfare of the population in the health sector. Life expectancy is closely related to infant mortality rate. Theoretically, decreasing of infant mortality rate will cause increasing of life expectancy. A statistical method that can be used to model life expectancy is nonparametric regression model based on least square spline estimator. This method provides high flexibility to accommodate pattern of data by using smoothing technique. The best estimated model is order one spline model with one knot based on minimum generalized cross validation (GCV) value of 0.607. Each increasing of one infant mortality rate unit will cause decreasing of life expectancy of 0.2314 for infant mortality rate less than 27, and of 0.0666 for infant mortality rate more than and equals to 27. In addition, based on mean square error (MSE) of 0.492 and R2value of 76.59% for nonparametric model approach compared with MSE of 0.634 and R2 value of 71.8% for parametric model approach, we conclude that the use of nonparametric model approach based on least square spline estimator is better than that of parametric model approach.

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“…Chamidah and Eridani [10] in the P-spline estimator. Chamidah and Lestari [11] in spline smoothing estimator. Aydin et., al.…”

Section: Introductionmentioning

confidence: 99%

Ability of Covariance Matrix in Bi-Response Multi-Prredictor Penalized Spline Model Through Longitudinal Data Simulation

Islamiyati¹,

Fatmawati²,

Chamidah³

2019

Preprint

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Bi-response longitudinal data is assumed to have a correlation between responses and observations on the same subject. This causes a correlation between errors. To overcome this problem, we can use a penalized spline model that involves weighting. In this study, the weight used is the covariance matrix. Based on longitudinal data simulations that contain two responses and three predictors, a small GCV value is obtained from the penalized spline model that involves the covariance matrix. This value is compared with the penalized spline model without the covariance matrix. This shows that we need to involve a covariance matrix in estimating bi-response multi-predictor longitudinal data with a penalized spline model.

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Spline Estimator in Homoscedastic Multi-Response Nonparametric Regression Model in Case of Unbalanced Number of Observations

Cited by 25 publications

References 0 publications

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

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

Analisis Pengaruh Angka Kematian Bayi Terhadap Angka Harapan Hidup Di Provinsi Jawa Timur Berdasarkan Estimator Least Square Spine

Ability of Covariance Matrix in Bi-Response Multi-Prredictor Penalized Spline Model Through Longitudinal Data Simulation

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