On Multiresponse Semiparametric Regression Model

Abstract

The modeling between predictors and response in statistics sometimes deals with more than one response or multiresponse situation. Furthermore, it can be happen that some predictors have linear relationship with the responses and the others predictor have unknown relationship. To overcome this modeling problem we proposed multiresponse semiparametric regression model. This model has more than one response and contains both parametric and nonparametric model. This study focuses on how to estimate parameter in multiresponse semiparametric regression. The weighted penalized least squares method is used to fit the model. This method produce partial spline estimator for nonparametric model and by applying some assumptions the estimator is polynomial natural spline. The performance of this estimator depends on smoothing parameter. So, we also proposed G criteria as modification of generalized cross validation in the context of multiresponse semiparametric regression to choose the optimal smoothing parameter. Using simulation data, it can be shown that this model can work well to describe relationship between some predictors and several responses.