Estimation of children growth curve based on kernel smoothing in multi-response nonparametric regression

Chamidah, Nur; Saifudin, Toha

doi:10.12988/ams.2013.13168

Cited by 28 publications

(12 citation statements)

References 3 publications

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“…e form of the function is unknown and approached using the kernel estimator. e function f h (t i ) for h � 1, 2 can be approached by the Taylor series with t around t 0 as follows [9]:…”

Section: Resultsmentioning

confidence: 99%

“…e spline nonparametric regression has been developed by Eubank [3], Becher et al [4], and Wang et al [5]. Hall and Huang [6], Okumura and Naito [7], Du et al [8], Chamidah and Saifudin [9], and Erçelik and Nadar [10] developed kernel nonparametric regression. Bilodeau [11] and Amato et al [12] estimated the nonparametric regression function with the Fourier series function.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Rahmawati

Budiantara

Prastyo

et al. 2021

International Journal of Mathematics and Mathematical Sciences

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Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

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“…e form of the function is unknown and approached using the kernel estimator. e function f h (t i ) for h � 1, 2 can be approached by the Taylor series with t around t 0 as follows [9]:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Rahmawati

Budiantara

Prastyo

et al. 2021

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…The purpose of modeling using regression analysis is to find the appropriate form of regression curve estimation [6]. Many nonparametric regression curve estimators have been developed by researchers, including Spline [2], [7]- [11], Kernel [12]- [15], and Fourier series [16]- [20].…”

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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“…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%

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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Estimation of children growth curve based on kernel smoothing in multi-response nonparametric regression

Cited by 28 publications

References 3 publications

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression

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

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

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