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Testing monotonicity via local least concave majorants

Akakpo, Nathalie; Balabdaoui, Fadoua; Durot, Cécile (2014), Testing monotonicity via local least concave majorants, Bernoulli, 20, 2, p. 514-544. http://dx.doi.org/10.3150/12-BEJ496

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1403.1699v1
Date
2014
Journal name
Bernoulli
Volume
20
Number
2
Publisher
Bernoulli Society
Pages
514-544
Publication identifier
http://dx.doi.org/10.3150/12-BEJ496
Metadata
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Author(s)
Akakpo, Nathalie
Balabdaoui, Fadoua
Durot, Cécile
Abstract (EN)
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.
Subjects / Keywords
Adaptivity; Least concave majorant; Monotonicity; Multiple test; Non-parametric; Uniform separation rate

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