Estimation of Regression Function in Multi-Response Nonparametric Regression Model Using Smoothing Spline and Kernel Estimators

The functions which describe relationship of more than one response variables observed at several values of the predictor variables in which there are correlations among the responses can be estimated by using a multi-response nonparametric regression model approach. In this study, we discuss about how we estimate the regression function of the multi-response nonparametric regression model by using both smoothing spline and kernel estimators. The principal objective is determining the smoothing spline and kernel estimators to estimate the regression function of the multi-response nonparametric regression model. The obtained results show that the regression functions obtained by using smoothing spline and kernel estimators are mathematically just distinguished by their smoother matrices. In addition, they are linear in observation and bias estimators.