• Bernoulli
  • Volume 20, Number 2 (2014), 514-544.

Testing monotonicity via local least concave majorants

Nathalie Akakpo, Fadoua Balabdaoui, and Cécile Durot

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We propose a new testing procedure for detecting localized departures from monotonicity of a signal embedded in white noise. In fact, we perform simultaneously several tests that aim at detecting departures from concavity for the integrated signal over various intervals of different sizes and localizations. Each of these local tests relies on estimating the distance between the restriction of the integrated signal to some interval and its least concave majorant. Our test can be easily implemented and is proved to achieve the optimal uniform separation rate simultaneously for a wide range of Hölderian alternatives. Moreover, we show how this test can be extended to a Gaussian regression framework with unknown variance. A simulation study confirms the good performance of our procedure in practice.

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Bernoulli, Volume 20, Number 2 (2014), 514-544.

First available in Project Euclid: 28 February 2014

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adaptivity least concave majorant monotonicity multiple test non-parametric uniform separation rate


Akakpo, Nathalie; Balabdaoui, Fadoua; Durot, Cécile. Testing monotonicity via local least concave majorants. Bernoulli 20 (2014), no. 2, 514--544. doi:10.3150/12-BEJ496.

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Supplemental materials

  • Supplementary material: Supplement to “Testing monotonicity via local least concave majorants”. We collect in the supplement [1] the most technical proofs. Specifically, we prove how to reduce to the case $\sigma=1$, we prove (19) and we provide a detailed proof for (17) and all results in Section 4.