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New designs to consistently estimate the isotonic regression

Author

Listed:
  • Ana Colubi

    (Universidad de Oviedo)

  • J. Santos Dominguez-Menchero

    (Universidad de Oviedo)

  • Gil Gonzalez-Rodriguez

    (Universidad de Oviedo)

Abstract

The usual estimators of the regression under isotonicity assumptions are too sensitive at the tails. In order to avoid this problem, some new strategies for fixed designs are analyzed. The uniform consistency of certain estimators on a closed and bounded working interval are obtained. It is shown that the usual isotonic regression can be employed when the number of observations at the edges of the interval is suitably controlled. Moreover, two modifications are proposed which substantially improve the results. One modification is based on the reallocation of part of the edge observations, and the other one forces the isotonic regression to take values within some horizontal bands. The theoretical results are complemented with some examples and simulation studies that illustrate the performance of the proposed estimators in practice.

Suggested Citation

  • Ana Colubi & J. Santos Dominguez-Menchero & Gil Gonzalez-Rodriguez, 2018. "New designs to consistently estimate the isotonic regression," Computational Statistics, Springer, vol. 33(2), pages 639-658, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-018-0792-0
    DOI: 10.1007/s00180-018-0792-0
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    References listed on IDEAS

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    1. Groeneboom, Piet & Jongbloed, Geurt, 2010. "Generalized continuous isotonic regression," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 248-253, February.
    2. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    3. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
    4. L. Yeganova & W. J. Wilbur, 2009. "Isotonic Regression under Lipschitz Constraint," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 429-443, May.
    5. Ana Colubi & J. Santos Domínguez‐Menchero & Gil González‐Rodríguez, 2006. "Testing Constancy for Isotonic Regressions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 463-475, September.
    6. Pal, Jayanta Kumar, 2008. "Spiking problem in monotone regression: Penalized residual sum of squares," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1548-1556, September.
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