Inverse boosting for monotone regression functions

A new method for the estimation of smooth monotone regression functions is proposed. It is assumed that the monotonicity may come from some physical or economic reason. A monotone estimator of an integral (of a positive function) using a gradient boosting method is derived. The proposed method generates a sequence of fits without monotone constraints and combines them to form a monotone estimate. An advantage of the proposed algorithm is that one can use a popular smoothing technique without the monotone constraint as the base learner. The performance of the proposed procedure is demonstrated on both simulated and real data sets.