Improving of classification accuracy of cyst and tumor using local polynomial estimator

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.

Health Card that is in Indonesia called as Kartu Menuju Sehat (KMS) is used to asses nutritional status of children up to five years old. The anthropometric index recorded in the Health Card is weight for age. The goal of this paper is to design standard growth charts for both boy and girl of weight for age of children in East Java, Indonesia. These growth charts are used to assess nutritional status of children in East Java, Indonesia. The rate of growth of weight is not the same for every interval of ages. For this case, the using of local linear estimator is suitable to design standard growth charts of weight for age of children up to five years old. The results show that the average values of R-square are 99.72% for boy and 99.73% for girl. Also, the average values of mean square error are 0.02758 for boy and 0.02976 for girl. In addition, the standard growth charts for both boy and girl of weight for age of children up to five years old in East Java, Indonesia is lower than those of WHO-2005 standard charts.

Wasting is a condition of a children characterized by a lack of weight by measuring weight for height. Currently, to monitor the growth conditions for childrens in Indonesia, we use the Towards Healthy Card called as Kartu Menuju Sehat (KMS) which is guided by WHO 2005. The samples used to design WHO-2005 standard charts are children from Brazil, Ghana, India, USA, Norway, and Oman that have different physical conditions from children in Indonesia. Therefore, the using of standards growth charts from other countries cause incompatibility with Indonesian’s children growth. To illustrate the growth patterns of children in East Java, we use the semiparametric least square spline estimator that gives more flexible pattern. In this study we used weight (kg) as a response variable, height (cm) as a predictor variable for nonparametric component, and gender as a predictor variable for parametric component. The results show the semiparametric least square spline estimator can explain the growth patterns of children well because it has determination coefficient (R²) of 99.78% and mean square error (MSE) of 0.0353. The standard chart of weight for height of boy is higher than that of girl and percentage of wasting nutritional status of girl greater than that of boy.