3 problems

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Optimality conjecture for adaptive Sobolev testing rates in dimension greater than one
Optimality conjecture. When $d>1$ , these rates are also optimal. The rate is known to be optimal for $d=1$ in several related models, whereas the source leaves the higher-dimension…
Conjectureopennonparametric-testing poisson-processes sobolev-spacesarXiv posted 2 days ago
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Conjecture on the disappearance of differences in power rates for other alternatives
Let $\nu^\dag$ be a fixed multi-index and consider testing the parametric model using local polynomial residual quantile estimators under alternatives of the form … For…
Conjectureopennonparametric-testing quantile-regressionarXiv posted 2 days ago
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Conjectured optimality of adaptive separation rates for anisotropic Nikol'skii-Besov balls
The paper considers adaptive two-sample tests for Poisson processes, with alternatives whose difference belongs to Besov, weak Besov, Sobolev, or anisotropic Nikol'skii-Besov class…
Conjectureopenbesov-spaces nonparametric-testing poisson-processesarXiv posted 2 days ago

Optimality conjecture for adaptive Sobolev testing rates in dimension greater than one