Geodesic
Consistency of the risk estimate of the multiple hypothesis testing with the FDR threshold
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2017), pp. 5-16 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the method of denoising the sparse signals based on the multiple hypothesis testing with the use of the FDR threshold. In the model with a white Gaussian noise we prove the consistency of the unbiased mean-square risk estimator.
Keywords: multiple hypothesis testing, thresholding, risk estimate, consistency. 
@article{VTPMK_2017_1_a0,
     author = {A. Yu. Zaspa and O. V. Shestakov},
     title = {Consistency of the risk estimate of the multiple hypothesis testing with the {FDR} threshold},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--16},
     year = {2017},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a0/}
}
TY  - JOUR
AU  - A. Yu. Zaspa
AU  - O. V. Shestakov
TI  - Consistency of the risk estimate of the multiple hypothesis testing with the FDR threshold
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2017
SP  - 5
EP  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a0/
LA  - ru
ID  - VTPMK_2017_1_a0
ER  - 
%0 Journal Article
%A A. Yu. Zaspa
%A O. V. Shestakov
%T Consistency of the risk estimate of the multiple hypothesis testing with the FDR threshold
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2017
%P 5-16
%N 1
%U http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a0/
%G ru
%F VTPMK_2017_1_a0
A. Yu. Zaspa; O. V. Shestakov. Consistency of the risk estimate of the multiple hypothesis testing with the FDR threshold. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2017), pp. 5-16. http://geodesic.mathdoc.fr/item/VTPMK_2017_1_a0/

[1] Donoho D., Johnstone I. M., “Ideal spatial adaptation via wavelet shrinkage”, Biometrika, 81:3 (1994), 425-455 | DOI | MR | Zbl

[2] Donoho D., Johnstone I., “Adapting to unknown smoothness via wavelet shrinkage”, Journal of the American Statistical Association, 90 (1995), 1200-1224 | DOI | MR | Zbl

[3] Donoho D., Johnstone I. M., “Minimax estimation via wavelet shrinkage”, Annals of Statistics, 26:3 (1998), 879-921 | DOI | MR | Zbl

[4] Jansen M., Noise Reduction by Wavelet Thresholding, Lecture Notes in Statistics, 161, Springer, New York, 2001 | DOI | MR | Zbl

[5] Markin A. V., Shestakov O. V., “Consistency of risk estimation with thresholding of wavelet coefficients”, Moscow University Computational Mathematics and Cybernetics, 34:1 (2010), 22-30 | DOI | MR | Zbl

[6] Shestakov O. V., “Asymptotic normality of adaptive wavelet thresholding risk estimation”, Doklady Mathematics, 86:1 (2012), 556-558 | DOI | MR | Zbl

[7] Shestakov O. V., “Central limit theorem for generalized cross-validation function in wavelet thresholding method”, Informatics and its Applications, 7:2 (2013), 40-49 (in Russian)

[8] Shestakov O. V., “On the strong consistency of the adaptive risk estimator for wavelet thresholding”, Journal of Mathematical Sciences, 214:1 (2016), 115-118 | DOI | MR | Zbl

[9] Mallat S., A Wavelet Tour of Signal Processing, Academic Press, NY, 1999, 857 pp. | MR | Zbl

[10] Benjamini Y., Hochberg Y., “Controlling the false discovery rate: a practical and powerful approach to multiple testing”, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 57 (1995), 289-300 | MR | Zbl

[11] Abramovich F., Benjamini Y., Donoho D., Johnstone I., “Adapting to unknown sparsity by controlling the false discovery rate”, Annals of Statistics, 34:2 (2006), 584-653 | DOI | MR | Zbl

[12] Hoeffding W., “Probability inequalities for sums of bounded random variables”, Journal of the American Statistical Association, 58:301 (1963), 13-30 | DOI | MR | Zbl