Corpus ID: 88522403

Minimax $L_2$-Separation Rate in Testing the Sobolev-Type Regularity of a function

  title={Minimax \$L_2\$-Separation Rate in Testing the Sobolev-Type Regularity of a function},
  author={Maurilio Gutzeit},
  journal={arXiv: Statistics Theory},
  • Maurilio Gutzeit
  • Published 2019
  • Mathematics
  • arXiv: Statistics Theory
  • In this paper we study the problem of testing if an $L_2-$function $f$ belonging to a certain $l_2$-Sobolev-ball $B_t(R)$ of radius $R>0$ with smoothness level $t>0$ indeed exhibits a higher smoothness level $s>t$, that is, belongs to $B_s(R)$. We assume that only a perturbed version of $f$ is available, where the noise is governed by a standard Brownian motion scaled by $\frac{1}{\sqrt{n}}$. More precisely, considering a testing problem of the form $$H_0:~f\in B_s(R)~~\mathrm{vs.}~~H_1:~f\in… CONTINUE READING


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