Detection of a Sparse Variable Function
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2302-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2302-z | ||
| 245 | 0 | 0 | |a Detection of a Sparse Variable Function |h [Elektronische Daten] |c [Yu. Ingster, I. Suslina] |
| 520 | 3 | |a We observe an unknown d-variable function f = f(t), t = (t 1, . . . , t d) ∈ [0, 1] d , f ∈ L 2([0, 1] d ), in Gaussian white noise of level ε > 0. We test the null hypothesis H 0 : f = 0 against an alternative H 1. Under the alternative, we assume that the unknown function is separated from zero: f ≥ r ε $$ \left\Vert f\right\Vert \ge {r}_{\varepsilon } $$ for some positive family r ε → ε → 0 0 $$ {r}_{\varepsilon}\underset{\varepsilon \to 0}{\to }0 $$ . Moreover, we assume that the unknown d-variable function f is a function of a smaller number of variables s ("sparse variable” function) that satisfies some regularity constraints. We also consider the problem of adaptation in k = 1, . . . , s. We assume that d = d ε → ∞. The integer s ∈ ℕ is either fixed or s = s ε → ∞, s = o(d). We study minimax error probabilities and obtain minimax separation rates that provide distinguishability in the problems. Then we apply the results obtained in the case of alternatives from Sobolev balls with a deleted L 2-ball. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Ingster |D Yu |u St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, Russia |4 aut | |
| 700 | 1 | |a Suslina |D I. |u St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, Russia |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/2(2015-04-01), 181-196 |x 1072-3374 |q 206:2<181 |1 2015 |2 206 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2302-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2302-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ingster |D Yu |u St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Suslina |D I. |u St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/2(2015-04-01), 181-196 |x 1072-3374 |q 206:2<181 |1 2015 |2 206 |o 10958 | ||