Spline estimator for bi-responses nonparametric regression model for longitudinal data

Fernandes, Adji Achmad Rinaldo; Budiantara, I Nyoman; Otok, Bambang Widjanarko; Suhartono, Suhartono

doi:10.12988/ams.2014.47566

Cited by 24 publications

(20 citation statements)

References 10 publications

(15 reference statements)

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“…Nonparametric regression is a regression model approached used if the pattern of relation between predictor variable and response isn't known, or if there is no complete past information on the shape of data pattern [1], [2], [3]. The nonparametric regression models which receive a lot of attention from re-I Nyoman Budiantara et al searchers are Kernel [4], [5], [6], Spline smoothing [2], [7], [8], [9], [10], Fourier Series [11], [12], [13] and Local Polynomial [14], [15]. Nonparametric regression approach has high flexibility because data is expected to look for its shape of regression curve estimation without being influenced by researchers subjective factors [1], [3], [6].…”

Section: Introductionmentioning

confidence: 99%

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The combination of spline and kernel estimator for nonparametric regression and its properties

Budiantara¹,

Ratnasari²,

Ratna³

et al. 2015

ams

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Consider additive nonparametric regression model with two predictor variables components. In the first predictor component, the regression curve is approached using Spline regression, and in the second predictor component, the regression curve is approached using Kernel regression. Random error of regression model is assumed to have independent normal distribution with zero mean and the same variance. This article provides an estimator of Spline regression curve, estimator of Kernel regression curve, and an estimator of a combination of Spline and Kernel regressions. The produced estimators are biased estimators, but all estimators are classified as linear estimators in observation. Estimator of a combination of Spline and Kernel regression depended on knot points and bandwith parameter. The best estimator of a combination of Spline and Kernel regression is found by minimizing Generalized Cross Validation (GCV) function.

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Section: Introductionmentioning

confidence: 99%

“…Estimator spline truncated has high flexibility [1]. Spline truncated also has very good ability to handle data with changeable behaviors on certain sub-intervals [1], [3], [8], [9], [10]. Kernel estimator in nonparametric and semiparametric regression lately also receive a lot of attention from researchers.…”

Section: Introductionmentioning

confidence: 99%

The combination of spline and kernel estimator for nonparametric regression and its properties

Budiantara¹,

Ratnasari²,

Ratna³

et al. 2015

ams

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, with biresponses approach, it will accommodate any correlation between each response variable. Fernandes et al (2014a) has been solved the RKHS for bi-responses and Fernandes et al (2014b) for multi-predictors.…”

Section: Introductionmentioning

confidence: 99%

Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data

Fernandes¹,

Budiantara²,

Otok³

et al. 2015

Journal of Mathematics and Statistics

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Nonparametric regression approach is used when the shape of the curve regression is unknown. The spline estimator approach for longitudinal data can accommodate the correlation between observations within the same subject, which is not found in the cross-section data, so that the autocorrelation assumption problem can be resolved. On the other hand, with bi-responses approach, it will accommodate any correlation between each response variables. The purposes of this study are (1) to obtain the function form of the nonparametric bi-responses and multipredictorsregression on longitudinal data, (2) to obtain the spline estimator in estimating the nonparametric bi-responses and multipredictorsregression curve on longitudinal data and (3) to apply the spline estimator in estimating the curve of nonparametric bi-responses and multi-predictorsregression on longitudinal data. Bi-responses and multipredictors nonparametric regression of the spline estimator on longitudinal data which meet the criteria of minimizing Penalized Weighted Least Square (PWLS). Application of data set (Patient in Pulmonary Tuberculosis) result shows that the spline estimator can be applied which gives the value of R 2 of 97.77%.

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“…Moreover, the advantage of spline is able to describe the change of the function pattern in the sub-specified interval and can handle well the data pattern which is dramatically change by using knots [5]. Some recently researches about the application of spline in nonparametric regression could be found in Lestari, Budiantara, Sunaryo and Mashuri [6], Wibowo, Haryatmi and Budiantara [7], and Fernandes, Budiantara, Otok and Suhartono [8].…”

Section: Introductionmentioning

confidence: 99%

Combined estimator Fourier series and spline truncated in multivariable nonparametric regression

Sudiarsa¹,

Budiantara²,

Suhartono³

et al. 2015

ams

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Multivariable additive nonparametric regression model is a nonparametric regression model that involves more than one predictor and has additively separable function on each predictor. There are many functions that can be used on nonparametric regression models, such as the kernel, splines, wavelets, local polynomial and fourier series. The purpose of this study is to obtain an estimator of multivariable additive nonparametric regression model. This research focuses on multivariable additive nonparametric regression model which is a combination between fourier series and spline truncated. The estimation method that be used to obtain the estimators is Penalized Least Square. This method requires the estimation of smoothing parameters in the optimization process to obtain the estimators of model. In 4998 I. Wayan Sudiarsa et al. this study, the derivation process for obtaining the estimator of multivariable additive nonparametric regression model has been successfully obtained, which consists of an estimator of fourier series and spline truncated. The results of this theoretical study shows that the Penalized Least Square method works simultaneously for obtaining the estimators of the smoothing parameter and nonparametric regression model parameters as a result of combining between fourier series and spline truncated which are additively separable.

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Spline estimator for bi-responses nonparametric regression model for longitudinal data

Abstract: The simulation results show that the spline estimator can be applied to the generation of data with m = 4 (cubic spline) which gives the value of R 2 of 94.63%.

Cited by 24 publications

References 10 publications

The combination of spline and kernel estimator for nonparametric regression and its properties

The combination of spline and kernel estimator for nonparametric regression and its properties

Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data

Combined estimator Fourier series and spline truncated in multivariable nonparametric regression

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