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Smoothness testing in the Sobolev sense
We want to develop a test to determine whether a function lying in a fixed L2-Sobolev-type ball of smoothness t, and generating a noisy signal, is in fact of a given smoothness s larger than 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, but that are very close to s-smooth functions. This problem has been considered in the case of specific Besov bodies where it is easier, and we plan to extend it to more usual Sobolev ellipsoids.


Smoothness testing

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