A convergent algorithm for a generalized multivariate isotonic regression problem
Files
Issue Date
Authors
Advisor
Citation
Hansohm, Jèurgen, and Xiaomi Hu. 2012. "A convergent algorithm for a generalized multivariate isotonic regression problem". Statistical Papers. 53 (1): 107-115.
Abstract
Sasabuchi et al. (Biometrika 70(2):465-472, 1983) introduces a multivariate version of the well-known univariate isotonic regression which plays a key role in the field of statistical inference under order restrictions. His proposed algorithm for computing the multivariate isotonic regression, however, is guaranteed to converge only under special conditions (Sasabuchi et al., J Stat Comput Simul 73(9):619-641, 2003). In this paper, a more general framework for multivariate isotonic regression is given and an algorithm based on Dykstra's method is used to compute the multivariate isotonic regression. Two numerical examples are given to illustrate the algorithm and to compare the result with the one published by Fernando and Kulatunga (Comput Stat Data Anal 52:702-712, 2007).