2012/11/16 by Arnaud Guyader, Guyader, Arnaud, Nicolas Jégou +7 · 1 citation
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1211.3930
25 pages, 5 figures
openalex publication_date 2012/11/16 · arxiv created 2012/11/19 · arxiv updated 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. As iterating the algorithm leads to overfitting, several practical stopping criteria are also presented and discussed.