A geometrical approach to Iterative Isotone Regression

In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic regression and the estimation of additive models. A geometrical interpretation enables us to link this iterative method with Von Neumann’s algorithm. Moreover, making a connection with the general property of isotonicity of projection onto convex cones, we derive another equivalent algorithm and go further in the analysis. Index Terms — Nonparametric estimation, Isotonic regression, Additive models, Metric projection onto convex cones. 2010 Mathematics Subject Classification: 52A20, 62G08, 90C33.