Statistical Papers

, Volume 53, Issue 1, pp 107–115

A convergent algorithm for a generalized multivariate isotonic regression problem

Regular Article

DOI: 10.1007/s00362-010-0317-6

Cite this article as:
Hansohm, J. & Hu, X. Stat Papers (2012) 53: 107. doi:10.1007/s00362-010-0317-6

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).

Keywords

Multivariate isotonic regressionProjectionDykstra’s algorithmPartial orderLeast squares solution

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.University of the Federal Armed ForcesMunichGermany
  2. 2.Department of Mathematics and StatisticsWichita State UniversityWichitaUSA