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.
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%.
Penalized regression procedures have become a very popular approach to estimating the curve of nonparametric regression in longitudinal data. Reproducing Kernel Hilbert Space (RKHS) is Reproducing Kernel Hilbert Space (RKHS) play a central role in Penalized Regression as a form and estimator function of the model. The aim of this study are to solve the estimation of Penalized Regression using RKHS, and apply the Penalized Regresion using secondary dataset. The Penalized Regresssion using RKHS is ** 1952 Adji Achmad Rinaldo Fernandes et al. The aplication of data 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 97.77%.
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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