Estimating Regression Function of Multi-response Semiparametric Regression Model Using Smoothing Spline

Lestari, Budi; Chamidah, Nur

doi:10.35741/issn.0258-2724.55.5.26

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…One of these smoothing techniques is the smoothing spline approach. In recent years, studies on smoothing splines have attracted a great deal of attention and the methodology has been widely used in many areas of research, for example, for estimating regression functions of nonparametric regression models, in [34,35] used smoothing spline, mixed smoothing spline, and Fourier series; estimating regression functions were conducted by [36,37] for a semiparametric nonlinear regression model and a semiparametric regression model; and smoothing spline in an ANOVA model was discussed by [38]. Smoothing spline estimator, with its powerful and flexible properties, is one of the most popular estimators used for estimating regression function of the nonparametric regression model.…”

Section: Introductionmentioning

confidence: 99%

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

et al. 2022

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In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. The relationship between these variables is expressed by a regression function. In the multiresponse nonparametric regression (MNR) model that is part of the multiresponse regression model, estimating the regression function becomes the main problem, as there is a correlation between the responses such that it is necessary to include a symmetric weight matrix into a penalized weighted least square (PWLS) optimization during the estimation process. This is, of course, very complicated mathematically. In this study, to estimate the regression function of the MNR model, we developed a PWLS optimization method for the MNR model proposed by a previous researcher, and used a reproducing kernel Hilbert space (RKHS) approach based on a smoothing spline to obtain the solution to the developed PWLS optimization. Additionally, we determined the symmetric weight matrix and optimal smoothing parameter, and investigated the consistency of the regression function estimator. We provide an illustration of the effects of the smoothing parameters for the estimation results using simulation data. In the future, the theory generated from this study can be developed within the scope of statistical inference, especially for the purpose of testing hypotheses involving multiresponse nonparametric regression models and multiresponse semiparametric regression models, and can be used to estimate the nonparametric component of a multiresponse semiparametric regression model used to model Indonesian toddlers' standard growth charts.

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Section: Introductionmentioning

confidence: 99%

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

et al. 2022

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“…However, those researchers discussed estimators in uni-response semiparametric regression (USR) models only. However, there are several researchers who have discussed estimators in a multiresponse semiparametric regression (MSR) model; for examples [39] studied estimating MSR using a smoothing spline estimator; [40] discussed determining confidence interval for the parameter of a parametric component of binary response SR model using truncated spline estimator; [41] discussed estimating the regression function and confidence interval of a parameter MSR model using a smoothing spline estimator. Furthermore, [42] discussed estimating the confidence interval for parameters of a MMSR model using a truncated spline estimator.…”

Section: Introductionmentioning

confidence: 99%

Consistency and Asymptotic Normality of Estimator for Parameters in Multiresponse Multipredictor Semiparametric Regression Model

et al. 2022

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A multiresponse multipredictor semiparametric regression (MMSR) model is a combination of parametric and nonparametric regressions models with more than one predictor and response variables where there is correlation between responses. Due to this correlation we need to construct a symmetric weight matrix. This is one of the things that distinguishes it from the classical method, which uses a parametric regression approach. In this study, we theoretically developed a method of determining a confidence interval for parameters in a MMSR model based on a truncated spline, and investigating asymptotic properties of estimator for parameters in a MMSR model, especially consistency and asymptotic normality. The weighted least squares method was used to estimate the MMSR model. Next, we applied a pivotal quantity method, a Cramer–Wold theorem, and a Slutsky theorem to determine the confidence interval, investigate consistency, and asymptotic normality properties of estimator for parameters in a MMSR model. The obtained results were that the estimated regression function is linear to observation. We also obtained a 100(1 − α)% confidence interval for parameters in the MMSR model, and the estimator for parameters in MMSR model was consistent and asymptotically normally distributed. In the future, these obtained results can be used as a theoretical basis in designing a standard toddlers growth chart to assess nutritional status.

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“…Hidayah et al (2019) used truncated splines applied in semiparametric regression. Lestari and Chamidah (2020) used a semiparametric model to smooth the spline.…”

mentioning

confidence: 99%

Platelet Modeling in DHF Patients Using Local Polynomial Semiparametric Regression on Longitudinal Data

Utami,

Chamidah,

Saifudin

2024

JTAM

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Regression analysis is one of the statistical methods used to model the relationship between response variables and predictor variables. Semiparametric regression is a combination of parametric and nonparametric regression. The estimator used in estimating the semiparametric regression model in this research is the Local Polynomial. Longitudinal data can be found in the health sector, including dengue hemorrhagic fever (DHF) data. The laboratory criteria for indication of DHF is thrombocytopenia. This research aims to obtain platelets model for DHF patients that can be used for forecasting so that it is hoped that it can provide information to the medical team in treating DHF patients. The estimated model used is Local Polynomial semiparametric regression on longitudinal data. The response variables in this research were platelets of DHF patients, which were influenced by hemoglobin as parametric predictor variable and examination time while hospitalized as nonparametric predictor variable. In the local polynomial regression model, it is necessary to select the optimal bandwidth and polynomial order method, GCV. The optimum bandwidth selection based on the GCV method obtained is 1.5 and polynomial order of 2, then applied to DHF patient platelet data, producing an estimated local polynomial semiparametric regression model that follows the actual data pattern. Modeling the platelets of DHF patients obtained using a local polynomial estimator resulted in an R2 value of 84.25% and MAPE of 4.5%, indicating highly accurate forecasting, so it can be concluded that the resulting model is better at predicting.

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Estimating Regression Function of Multi-response Semiparametric Regression Model Using Smoothing Spline

Cited by 4 publications

References 3 publications

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

Consistency and Asymptotic Normality of Estimator for Parameters in Multiresponse Multipredictor Semiparametric Regression Model

Platelet Modeling in DHF Patients Using Local Polynomial Semiparametric Regression on Longitudinal Data

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