2008/09/30 by Rudolf Beran, Lutz Dümbgen, Lutz Duembgen
Computer Science · Engineering · Mathematics · #Control Systems and Identification #Image and Signal Denoising Methods #Statistical and numerical algorithms #stat.CO #stat.ME
paper · pdf · doi:10.1007/s11222-009-9124-0
published as Statistics and Computing, Volume 20, Number 2 (2010), pp. 177-189
arxiv created 2009/01/26 · openalex publication_date 2009/04/23 · arxiv updated 2010/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by pairs (i,j) in 1,...,rx1,...,s. Various numerical examples illustrate our methods.