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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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/
@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

[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