Detection of a sparse submatrix of a high-dimensional noisy matrix

Bernoulli

Volumn 19, Issue 5 B, 2013, Pages 2652-2688

  Butucea, Cristina ^a,b   Ingster, Yuri I ^c  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b CREST   (France)

^c SAINT PETERSBURG ELECTROTECHNICAL UNIVERSITY LETI   (Russian Federation)

Author keywords

Detection of sparse signal; Minimax adaptive testing; Minimax testing; Random matrices; Sharp detection bounds

Indexed keywords

EID: 84891934985     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/12-BEJ470     Document Type: Article

References (11)

1. Addario-Berry, L., Broutin, N., Devroye, L. and Lugosi, G. (2010). On combinatorial testing problems. Ann. Statist. 38 3063-3092. MR2722464
2. Arias-Castro, E., Candès, E.J. and Durand, A. (2011). Detection of an anomalous cluster in a network. Ann. Statist. 39 278-304. MR2797847
3. Arias-Castro, E., Candès, E.J. and Plan, Y. (2010). Global testing and sparse alternatives: ANOVA, multiple comparisons and the higher criticism. Available at arXiv:1007.1434.
4. Arias-Castro, E., Donoho, D.L. and Huo, X. (2005). Near-optimal detection of geometric objects by fast multiscale methods. IEEE Trans. Inform. Theory 51 2402-2425. MR2246369
5. Bickel, P.J., Ritov, Y. and Tsybakov, A.B. (2009). Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 1705-1732. MR2533469
6. Donoho, D. and Jin, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32 962-994. MR2065195
7. Ingster, Y.I. (1997). Some problems of hypothesis testing leading to infinitely divisible distributions. Math. Methods Statist. 6 47-69. MR1456646
8. Ingster, Y.I. and Suslina, I.A. (2002). On a detection of a signal of known shape in multichannel system. Zapiski Nauchn. Sem. POMI 294 88-112 (in Russian) (transl. J. Math. Sci. 127 1723-1736).
9. Koltchinskii, V., Lounici, K. and Tsybakov, A.B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Statist. 39 2302-2329. MR2906869
10. Shabalin, A.A., Weigman, V.J., Perou, C.M. and Nobel, A.B. (2009). Finding large average submatrices in high dimensional data. Ann. Appl. Stat. 3 985-1012. MR2750383
11. Sun, X. and Nobel, A.B. (2010). On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix. Available at arXiv:1009.0562v1.