Semiparametric additive isotonic regression

We consider the efficient estimation in the semiparametric additive isotonic regression model where each additive nonparametric component is assumed to be a monotone function. We show that the least-square estimator of the finite-dimensional regression coefficient is root-n$n$ consistent and asymptotically normal. Moreover, the isotonic estimator of each additive functional component is proved to have the oracle property, which means the additive component can be estimated with the highest asymptotic accuracy as if the other components were known. A fast algorithm is developed by iterating between a cyclic pool adjacent violators procedure and solving a standard ordinary least squares problem. Simulations are used to illustrate the performance of the proposed procedure and verify the oracle property.