Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals View Full Text


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Article Info

DATE

2021-09-03

AUTHORS

Alexander I. Jordan, Anja Mühlemann, Johanna F. Ziegel

ABSTRACT

In general, the solution to a regression problem is the minimizer of a given loss criterion and depends on the specified loss function. The nonparametric isotonic regression problem is special, in that optimal solutions can be found by solely specifying a functional. These solutions will then be minimizers under all loss functions simultaneously as long as the loss functions have the requested functional as the Bayes act. For the functional, the only requirement is that it can be defined via an identification function, with examples including the expectation, quantile, and expectile functionals. Generalizing classical results, we characterize the optimal solutions to the isotonic regression problem for identifiable functionals by rigorously treating these functionals as set-valued. The results hold in the case of totally or partially ordered explanatory variables. For total orders, we show that any solution resulting from the pool-adjacent-violators algorithm is optimal. More... »

PAGES

1-26

References to SciGraph publications

  • 2011. Pathfinding through Congruences in RELATIONAL AND ALGEBRAIC METHODS IN COMPUTER SCIENCE
  • 1999-03. Algorithms for a Class of Isotonic Regression Problems in ALGORITHMICA
  • 2013-08-01. Isotonic Regression for Multiple Independent Variables in ALGORITHMICA
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    http://scigraph.springernature.com/pub.10.1007/s10463-021-00808-0

    DOI

    http://dx.doi.org/10.1007/s10463-021-00808-0

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