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Testing equality of functions under monotonicity constraints

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  • Cécile Durot
  • Piet Groeneboom
  • Hendrik P. Lopuhaä

Abstract

We consider the problem of testing equality of functions f j :[ a, b ]→ℝ for j =1, 2, ..., J on the basis of J independent samples from possibly different distributions under the assumption that the functions are monotone. We provide a uniform approach that covers testing equality of monotone regression curves, equality of monotone densities and equality of monotone hazards in the random censorship model. Two test statistics are proposed based on L 1 -distances. We show that both statistics are asymptotically normal and we provide bootstrap implementations, which are shown to have critical regions with asymptotic level α.

Suggested Citation

  • Cécile Durot & Piet Groeneboom & Hendrik P. Lopuhaä, 2013. "Testing equality of functions under monotonicity constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 939-970, December.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:939-970
    DOI: 10.1080/10485252.2013.826356
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    References listed on IDEAS

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    4. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2011. "Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 191-202.
    5. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    6. Piet Groeneboom, 2012. "Likelihood Ratio Type Two-Sample Tests for Current Status Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 645-662, December.
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    Cited by:

    1. Hendrik P. Lopuhaä & Eni Musta, 2017. "Smooth estimation of a monotone hazard and a monotone density under random censoring," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 58-82, January.
    2. Holger Dette & Subhra Sankar Dhar & Weichi Wu, 2021. "Identifying shifts between two regression curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 855-889, October.
    3. Jonas Peters & Peter Bühlmann & Nicolai Meinshausen, 2016. "Causal inference by using invariant prediction: identification and confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 947-1012, November.
    4. Lopuhaä, Hendrik P. & Musta, Eni, 2018. "The distance between a naive cumulative estimator and its least concave majorant," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 119-128.

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