Testing the regularity of a smooth signal

@article{Carpentier2015TestingTR,
  title={Testing the regularity of a smooth signal},
  author={A. Carpentier},
  journal={Bernoulli},
  year={2015},
  volume={21},
  pages={465-488}
}
We develop a test to determine whether a function lying in a fixed $L_2$-Sobolev-type ball of smoothness $t$, and generating a noisy signal, is in fact of a given smoothness $s\geq t$ or not. While it is impossible to construct a uniformly consistent test for this problem on every function of smoothness $t$, it becomes possible if we remove a sufficiently large region of the set of functions of smoothness $t$. The functions that we remove are functions of smoothness strictly smaller than $s… 

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