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On the convergence of row-modification algorithm for matrix projections

Author

Listed:
  • Hu, Xiaomi
  • Hansohm, Jürgen
  • Hoffmann, Linda
  • Zohner, Ye Emma

Abstract

This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper.

Suggested Citation

  • Hu, Xiaomi & Hansohm, Jürgen & Hoffmann, Linda & Zohner, Ye Emma, 2012. "On the convergence of row-modification algorithm for matrix projections," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 216-221.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:216-221
    DOI: 10.1016/j.jmva.2011.09.005
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    References listed on IDEAS

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    1. Fernando, W.T.P.S. & Kulatunga, D.D.S., 2007. "On the computation and some applications of multivariate isotonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 702-712, October.
    2. Hu, Xiaomi, 2009. "p-values of a test on homogeneous means in a multivariate isotonic regression," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2005-2011, October.
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    Cited by:

    1. Asfha, Huruy & Hu, Xiaomi, 2023. "An algorithm for a pseudo RMLE under simple tree multivariate order restriction," Statistics & Probability Letters, Elsevier, vol. 202(C).

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