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

Budiantara, I Nyoman; Ratnasari, Vita; Ratna, Madu; Zain, Ismaini

doi:10.12988/ams.2015.58517

Cited by 37 publications

(24 citation statements)

References 11 publications

(17 reference statements)

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“…The nonlinear structural model applied in this study is the structural model of SEM given by ( , ) = + 1 2 η ξ ξ ω f ω ω ζ (18) where, η ω is factor score vector of endogenous latent variables, ( , )…”

Section: The Estimation Of Nonlinear Structural Model Using Splinementioning

confidence: 99%

“…It uses the spline function to estimate the parameter of nonlinear structural model. Some researches about the spline function in nonparametric regression could be found in Fernandes, Budiantara, Otok and Suhartono [15], Lestari, Budiantara, Sunaryo and Mashuri [16], Wibowo, Haryatmi and Budiantara [17], Budiantara, Ratnasari, Ratna and Zain [18], and Sudiarsa, Budiantara, Suhartono and Purnami [19]. The proposed function involving knot was able at obtaining the information of the relation between latent variables which differs in the certain range.…”

Section: Introductionmentioning

confidence: 99%

“…nonlinear function and ζ is the error vector of structural model. Model mentioned in Eq (18). involves two exogenous latent variables and one endogenous latent variable that is assumed as an addition, so with using spline approach, model Eq.…”

mentioning

confidence: 99%

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Parameter estimation of nonlinear structural model SEM using spline approach

Ruliana¹,

Budiantara²,

Otok³

et al. 2015

ams

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Structural equation modeling (SEM) consists of two parts, namely measurement model, which measures a relation between indicators with latent variables and structural model that analyzes the relationships between the latent variables. In General, the researches about SEM assume that relation among latent variables are linear. If the relation between latent variables is nonlinear than the function has to be estimated. Two exogenous and an endogenous latent variables models can be written as follows (,) = + 1 2 1 2 ξ ξ ω ω ω and (,) = 1 2 κ κ κ. The estimator of the function in the nonlinear structural model is influenced by location and some knot points 1 κ and 2 κ. 7440 Ruliana et al.

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Section: The Estimation Of Nonlinear Structural Model Using Splinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parameter estimation of nonlinear structural model SEM using spline approach

Ruliana¹,

Budiantara²,

Otok³

et al. 2015

ams

Self Cite

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“…Spline is a form of estimator which is also often used in nonparametric regression because it has good visual interpretation, is flexible, and is able to handle character functions that are smooth (Eubank, 1988); (Budiantara, et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province

Mariati

Budiantara

Ratnasari

2021

ICSA

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In estimating the regression curve there are three approaches, namely parametric regression, nonparametric regression and semiparametric regression. Nonparametric regression approach has high flexibility. Nonparametric regression approach that is quite popular is Truncated Spline. Truncated Spline is a polynomial pieces which have segmented and continuous. One of the advantages of Spline is that it can handle data that changes at certain sub intervals, so this model tends to search for data estimates wherever the data pattern moves and there are points of knots. In reality, data patterns often change at certain sub intervals, one of which is data on poverty in the Papua Province. Papua Province is ranked first in the percentage of poor people in Indonesia. The best of model Truncated Spline in nonparametric regression for the poverty model in Papua Province is using a combination of knot.

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“…Therefore, if only one estimator is used to estimate the nonparametric regression curve, the estimator generated does not match the data pattern. As a result, the result regression model's estimation is less precise and tends to produce large errors (Budiantara et al, 2015). Based on the description explained, this study was conducted to model the percentage of malnourished children baby in the NTB Province using a nonparametric mixed truncated spline and kernel regression model.…”

Section: A Introductionmentioning

confidence: 99%

Spline and Kernel Mixed Nonparametric Regression for Malnourished Children Model in West Nusa Tenggara

Sauri

Hadijati

Fitriyani

2021

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Health sector development is essential to improve human life quality, especially in West Nusa Tenggara (NTB) Province. Based on data from the NTB Provincial Health Office from 2011 to 2016, children under five suffering from malnutrition continued to increase, caused by several factors that affected the incident. Therefore, appropriate analysis is needed to model children who suffer from malnutrition in NTB Province in 2016, consisting of 10 districts based on the variables that influence it. The analysis in this study was carried out using a nonparametric regression mixed-model spline truncated and kernel. The estimation of the nonparametric regression curve depends on the optimal knot points and bandwidths parameter. Therefore, in determining the optimal knot points and bandwidths obtained from Generalized Cross-Validation (GCV). Based on the analysis that has been done, we obtained a nonparametric regression mixed-model spline truncated and kernel optimal knot points, such as for each variable and optimum bandwidths, such as and , with the value of GCV. The mixed model acquired has a good model by considering the values of and MSE. Besides, the MAPE value indicated a high degree of accuracy, so that the model obtained has an excellent forecast.

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

Cited by 37 publications

References 11 publications

Parameter estimation of nonlinear structural model SEM using spline approach

Parameter estimation of nonlinear structural model SEM using spline approach

Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province

Spline and Kernel Mixed Nonparametric Regression for Malnourished Children Model in West Nusa Tenggara

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