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A convergent algorithm for a generalized multivariate isotonic regression problem

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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).

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Authors and Affiliations

  1. University of the Federal Armed Forces, Munich, Germany

    Jürgen Hansohm

  2. Department of Mathematics and Statistics, Wichita State University, Wichita, KS, 67260-0033, USA

    Xiaomi Hu

Authors
  1. Jürgen Hansohm
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  2. Xiaomi Hu
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Correspondence to Jürgen Hansohm.

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Hansohm, J., Hu, X. A convergent algorithm for a generalized multivariate isotonic regression problem. Stat Papers 53, 107–115 (2012). https://doi.org/10.1007/s00362-010-0317-6

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  • DOI: https://doi.org/10.1007/s00362-010-0317-6

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