Semi-parametric Additive Isotonic Regression Model

The semiparametric additive models are the promotion of the nonparametric models,they effectively balance the flexibility and the accuracy of the data,and are used in many fields,including medicine,economics,big data,etc.In this paper,we propose a new estimated method for the semiparametric additive regression models where each additive nonparametric function is assumed to be monotone and increasing.These monotonic functions are approximated by the Bernstein-Schoenberg splines with the isotonic constraint,and the estimation of the model is presented by the least squares method.We establish asymptotic properties for the resulting estimators of the parametric component,and the convergence rate of the nonparametric components.The finite sample performance of the proposed method is assessed by simulation studies,and demonstrated by the analyses of the Plasma data.The contents of the paper is as follows: Section 1 introduces two kinds of additive models and the work of this paper;Section 2 discusses estimated method of the semiparametric additive isotonic regression model,and gives The asymptotic properties of these estimators based on some assumption conditions.Section 3 provides a algorithm for solving the estimating functions and illustrates the estimation performance with simulation results.Section 4,we evaluate the proposed method by the plasma data.Section 5 gives the conclusions and a briefly future discussion.Technical proofs of the main results are found in the Appendix A.