In applications, we often meet the problem where more than one response variable is observed at several values of predictor variables, and these responses are correlated with each other. The multiresponse nonparametric regression model approach is appropriate to model the functions which represent relationship between response and predictor variables. This relationship is drawn by the regression function. The principal problem of this model approach is estimating of the regression function of this model. The spline estimator is one of the most popular estimators used for estimating it. In this paper we discuss methods to obtain a smoothing spline estimator for estimating the regression function, to get a covariance matrix estimator, and to choose an optimum smoothing parameter. In addition, we investigate the asymptotic properties of the smoothing spline estimator.
