Physical children growth is measured by using anthropometric measures i.e. weight, height and head circumference. The children around two years old grow rapidly, and than decrease slowly along with increasing of children age. It means that locally model approach is more appropriate to the data. Kernel smoothing is one of estimation methods in nonparametric regression. In this paper, we study about Kernel smoothing in multi-response nonparametric regression model and apply it for estimating children up to five years old growth. The model consists of three response variables i.e. weight, height and head circumference, and age as a predictor variable. For determining optimal bandwidth for each response variable, we use cross-validation method. Based on children data in Surabaya 2010, and the 50 th percentiles estimation of weight, height and head circumference versus age, we obtain the mean squared error value is 0.05583 and coefficient of determination is 99.99%. The estimation model of children growth curve based on multi-respon kernel smoothing shows fluctuation of the curve and gives mean squared error value tends to zero and coefficient of determination tends to one. These facts mean that the estimation has satisfied goodness of fit criterion.
The principle problem in multiresponse nonparametric regression model is how we estimate the regression functions which draw association between some dependent (response) variables and some independent (predictor) variables where there are correlations between responses. There are many techniques used to estimate the regression function. Two of them are spline and kernel smoothing techniques. Speaking about smoothing techniques, not only in uniresponse spline and kernel nonparametric regression models but also in multiresponse spline and kernel nonparametric regression models, the estimations of regression functions depend on smoothing parameters. In the privious researches the covariance matrices were assumed to be known. Matrix of covariance is not assumed known in this research. The goals of this research are selecting of optimal smoothing parameters for the model we consider through spline and kernel smoothing techniques. Optimal smoothing parameters can be obtained by taking the solution to generalized cross validation (GCV) optimization problem. The obtained results of this research are the optimal smoothing parameter for smoothing spline estimator approach and the optimal smoothing parameter namely optimal bandwidth for kernel estimator approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.