메뉴 건너뛰기




Volumn 7, Issue 1, 2013, Pages 1328-1368

Some optimality properties of FDR controlling rules under sparsity

Author keywords

Asymptotic optimality; Bayes risk; False discovery rate; Multiple testing; Two groups model

Indexed keywords


EID: 84884955624     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-EJS808     Document Type: Article
Times cited : (11)

References (44)
  • 1
    • 33746242092 scopus 로고    scopus 로고
    • Adapting to unknown sparsity by controlling the false discovery rate
    • MR2281879 MR2281879
    • Abramovich F., Benjamini Y., Donoho D. L. and Johnstone I. M. (2006). Adapting to unknown sparsity by controlling the false discovery rate. Ann. Statist. 34, 584-653. MR2281879 MR2281879
    • (2006) Ann. Statist. , vol.34 , pp. 584-653
    • Abramovich, F.1    Benjamini, Y.2    Donoho, D.L.3    Johnstone, I.M.4
  • 2
    • 0001677717 scopus 로고
    • Controlling the false discovery rate: A practical and powerful approach to multiple testing
    • MR1325392 MR1325392
    • Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B. 57, 289-300. MR1325392 MR1325392
    • (1995) J. Roy. Statist. Soc. Ser. B. , vol.57 , pp. 289-300
    • Benjamini, Y.1    Hochberg, Y.2
  • 3
    • 3142698408 scopus 로고    scopus 로고
    • Modifying the Schwarz Bayesian Information Criterion to locate multiple interacting quantitive trait loci
    • Bogdan, M., Ghosh, J. K., and Doerge, R. W. (2004). Modifying the Schwarz Bayesian Information Criterion to locate multiple interacting quantitive trait loci. Genetics 167, 989-999.
    • (2004) Genetics , vol.167 , pp. 989-999
    • Bogdan, M.1    Ghosh, J.K.2    Doerge, R.W.3
  • 5
    • 69049121784 scopus 로고    scopus 로고
    • A comparison of the Simes-Benjamini-Hochberg procedure with some Bayesian rules for multiple testing
    • Fetschrift in Honor of Professor Pranab K. Sen, edited by N. Balakrishnan, Edsel Peña and Mervyn J. Silvapulle, Beachwood Ohio. MR2462208
    • Bogdan, M., Ghosh, J. K. and Tokdar S. T. (2008). A comparison of the Simes-Benjamini-Hochberg procedure with some Bayesian rules for multiple testing. IMS Collections, Vol.1, Beyond Parametrics in Interdisciplinary Research: Fetschrift in Honor of Professor Pranab K. Sen, edited by N. Balakrishnan, Edsel Peña and Mervyn J. Silvapulle 211-230. Beachwood Ohio. MR2462208
    • (2008) IMS Collections, Vol.1, Beyond Parametrics in Interdisciplinary Research , pp. 211-230
    • Bogdan, M.1    Ghosh, J.K.2    Tokdar, S.T.3
  • 6
    • 84857648827 scopus 로고    scopus 로고
    • Asymptotic Bayes Optimality under sparsity of some multiple testing procedures
    • MR2850212
    • Bogdan, M., Chakrabati, A., Frommlet F. and Ghosh, J. K. (2011) Asymptotic Bayes Optimality under sparsity of some multiple testing procedures. Ann. Statist., 39, 1551-1579. MR2850212
    • (2011) Ann. Statist. , vol.39 , pp. 1551-1579
    • Bogdan, M.1    Chakrabati, A.2    Frommlet, F.3    Ghosh, J.K.4
  • 9
    • 73949087537 scopus 로고    scopus 로고
    • Optimal rates of convergence for estimating the null and proportion of non-null effects in large-scale multiple testing
    • MR2589318
    • Cai, T. and Jin, J. (2010). Optimal rates of convergence for estimating the null and proportion of non-null effects in large-scale multiple testing. Ann. Statist. 38, 100-145. MR2589318
    • (2010) Ann. Statist. , vol.38 , pp. 100-145
    • Cai, T.1    Jin, J.2
  • 10
    • 70249095757 scopus 로고    scopus 로고
    • False discovery rate control with multivariate p-values
    • MR2411440
    • Chi, Z. (2008). False discovery rate control with multivariate p-values. Electronic Journal of Statistics 2, 368-411. MR2411440
    • (2008) Electronic Journal of Statistics , vol.2 , pp. 368-411
    • Chi, Z.1
  • 12
    • 23744475601 scopus 로고    scopus 로고
    • Higher criticism for detecting sparse heterogeneous mixtures
    • MR2065195
    • Donoho, D. L. and Jin, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32, 962-994. MR2065195
    • (2004) Ann. Statist. , vol.32 , pp. 962-994
    • Donoho, D.L.1    Jin, J.2
  • 13
    • 34547291918 scopus 로고    scopus 로고
    • Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data
    • MR2329475
    • Donoho, D. L. and Jin, J. (2006). Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data. Ann. Statist. 34, 2980-3018. MR2329475
    • (2006) Ann. Statist. , vol.34 , pp. 2980-3018
    • Donoho, D.L.1    Jin, J.2
  • 14
    • 0012499079 scopus 로고
    • Minimax risk over lp-balls for lq-error
    • MR1278886
    • Donoho, D. L. and Johnstone, I. M. (1994). Minimax risk over lp-balls for lq-error. Probab. Theory Related Fields 99, 277-303. MR1278886
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 277-303
    • Donoho, D.L.1    Johnstone, I.M.2
  • 15
    • 0035992248 scopus 로고    scopus 로고
    • Empirical bayes methods and false discovery rates for microarrays
    • Efron, B. and Tibshirani, R. (2002). Empirical bayes methods and false discovery rates for microarrays. Genetic Epidemiology, 23, 70-86.
    • (2002) Genetic Epidemiology , vol.23 , pp. 70-86
    • Efron, B.1    Tibshirani, R.2
  • 16
    • 47749152434 scopus 로고    scopus 로고
    • Microarrays, Empirical Bayes and the two-group model
    • MR2431866
    • Efron, B. (2008). Microarrays, Empirical Bayes and the two-group model. Stat. Sci., 23(1), 1-22. MR2431866
    • (2008) Stat. Sci. , vol.23 , Issue.1 , pp. 1-22
    • Efron, B.1
  • 17
    • 38349049320 scopus 로고    scopus 로고
    • To how many simultaneous hypothesis tests can normal, Student's t or bootstrap calibration be applied?
    • MR2372536
    • Fan, J., Hall, P. and Yao, Q. (2007). To how many simultaneous hypothesis tests can normal, Student's t or bootstrap calibration be applied? J. Amer. Statist. Assoc., 102, 1282-1288. MR2372536
    • (2007) J. Amer. Statist. Assoc. , vol.102 , pp. 1282-1288
    • Fan, J.1    Hall, P.2    Yao, Q.3
  • 19
    • 65349123087 scopus 로고    scopus 로고
    • On the false discovery rate and an asymptotically optimal rejection curve
    • MR2502644
    • Finner, H., Dickhaus, T. and Roters, M. (2009). On the false discovery rate and an asymptotically optimal rejection curve. Ann. Statist. 37, 596-618. MR2502644
    • (2009) Ann. Statist. , vol.37 , pp. 596-618
    • Finner, H.1    Dickhaus, T.2    Roters, M.3
  • 20
    • 79959746046 scopus 로고    scopus 로고
    • Modified versions of Bayesian Information Criterion for genomewide association studies
    • MR2897552
    • Frommlet, F., Ruhaltinger, F., Twarog, P. and Bogdan, M. (2012). Modified versions of Bayesian Information Criterion for genomewide association studies. Comput. Stat. Data An., 56, 1038-1051. MR2897552
    • (2012) Comput. Stat. Data An. , vol.56 , pp. 1038-1051
    • Frommlet, F.1    Ruhaltinger, F.2    Twarog, P.3    Bogdan, M.4
  • 21
    • 0036020944 scopus 로고    scopus 로고
    • Operating characteristics and extensions of the false discovery rate procedure
    • MR1924303
    • Genovese, C. andWasserman, L. (2002). Operating characteristics and extensions of the false discovery rate procedure. J. R. Stat. Soc. Ser. B Stat. Methodol. 64(3), 499-517. MR1924303
    • (2002) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.64 , Issue.3 , pp. 499-517
    • Genovese, C.1    Wasserman, L.2
  • 22
    • 0001729472 scopus 로고    scopus 로고
    • Calibration and empirical Bayes variable selection
    • MR1813972
    • George, E. I. and Foster, D. P. (2000). Calibration and empirical Bayes variable selection. Biometrika 87, 731-747. MR1813972
    • (2000) Biometrika , vol.87 , pp. 731-747
    • George, E.I.1    Foster, D.P.2
  • 23
    • 50649094743 scopus 로고    scopus 로고
    • On optimality of the Benjamini-Hochberg procedure for the false discovery rate
    • MR2528629
    • Guo, W. and Rao, M. B. (2008). On optimality of the Benjamini-Hochberg procedure for the false discovery rate. Statistics and Probability Letters 78, 2024-2030. MR2528629
    • (2008) Statistics and Probability Letters , vol.78 , pp. 2024-2030
    • Guo, W.1    Rao, M.B.2
  • 24
    • 34250721552 scopus 로고    scopus 로고
    • Estimating the null and the proportion of non-null effects in large-scale multiple comparisons
    • MR2325113
    • Jin, J. and Cai, T. C. (2007). Estimating the null and the proportion of non-null effects in large-scale multiple comparisons. J. Amer. Statist. Assoc. 102, 495-506. MR2325113
    • (2007) J. Amer. Statist. Assoc. , vol.102 , pp. 495-506
    • Jin, J.1    Cai, T.C.2
  • 25
    • 84951382506 scopus 로고
    • Asymptotic behavior of Bayes tests and Bayes risk
    • MR0362588
    • Johnson, B. R. and Truax, D. R. (1973). Asymptotic behavior of Bayes tests and Bayes risk. Ann. Statist. 2, 278-294. MR0362588
    • (1973) Ann. Statist. , vol.2 , pp. 278-294
    • Johnson, B.R.1    Truax, D.R.2
  • 26
    • 3543030265 scopus 로고    scopus 로고
    • Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences
    • MR2089135
    • Johnstone, I. M. and Silverman, B. W. (2004). Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences. Ann. Statist. 32, 1594-1649. MR2089135
    • (2004) Ann. Statist. , vol.32 , pp. 1594-1649
    • Johnstone, I.M.1    Silverman, B.W.2
  • 27
    • 26444493657 scopus 로고    scopus 로고
    • EbayesThresh: R programs for empirical Bayes thresholding
    • Johnstone, I. M. and Silverman, B. W. (2005). EbayesThresh: R programs for empirical Bayes thresholding. J. Stat. Software 12, Issue 8.
    • (2005) J. Stat. Software , vol.12 , Issue.8
    • Johnstone, I.M.1    Silverman, B.W.2
  • 28
    • 0001799563 scopus 로고
    • A theory of some multiple decision problems, I
    • MR0084952
    • Lehmann, E. L. 1957. A theory of some multiple decision problems, I. Ann. Math. Stat. 28, 1-25. MR0084952
    • (1957) Ann. Mathc. Stat. , vol.28 , pp. 1-25
    • Lehmann, E.L.1
  • 29
    • 23744439164 scopus 로고    scopus 로고
    • Generalizations of the familywise error rate
    • MR2195631
    • Lehmann, E. L. and Romano, J. P. (2005). Generalizations of the familywise error rate. Ann. Statist. 33, 1138-1154. MR2195631
    • (2005) Ann. Statist. , vol.33 , pp. 1138-1154
    • Lehmann, E.L.1    Romano, J.P.2
  • 30
    • 23744494442 scopus 로고    scopus 로고
    • On optimality of stepdown and stepup multiple test procedures
    • MR2195629
    • Lehmann, E. L., Romano, J. P. and Popper Shaffer, J. (2005). On optimality of stepdown and stepup multiple test procedures. Ann. Statist. 33, 1084-1108. MR2195629
    • (2005) Ann. Statist. , vol.33 , pp. 1084-1108
    • Lehmann, E.L.1    Romano, J.P.2    Popper Shaffer, J.3
  • 31
    • 27944433393 scopus 로고    scopus 로고
    • Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
    • MR2275246 MR2275246
    • Meinshausen, N. and Rice, J. (2006). Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. Ann. Statist. 34, 373-393. MR2275246 MR2275246
    • (2006) Ann. Statist. , vol.34 , pp. 373-393
    • Meinshausen, N.1    Rice, J.2
  • 32
    • 77955482663 scopus 로고    scopus 로고
    • Accurate Prediction of Genetic Values for Complex Traits by Whole-Genome Resequencing
    • Meuwissen, T. and Goddard, M. (2010). Accurate Prediction of Genetic Values for Complex Traits by Whole-Genome Resequencing. Genetics 185 (2), 623-631
    • (2010) Genetics , vol.185 , Issue.2 , pp. 623-631
    • Meuwissen, T.1    Goddard, M.2
  • 34
    • 84858748167 scopus 로고    scopus 로고
    • Power-enhanced multiple decision functions controlling family-wise error and false discovery rates
    • MR2797856
    • Peña, E. A., Habiger, J. D., and Wu, W. (2011). Power-enhanced multiple decision functions controlling family-wise error and false discovery rates. Ann. Statist. 39(1), 556-583. MR2797856
    • (2011) Ann. Statist. , vol.39 , Issue.1 , pp. 556-583
    • Peña, E.A.1    Habiger, J.D.2    Wu, W.3
  • 35
    • 23044497824 scopus 로고    scopus 로고
    • Error Distribution for Gene Expression Data
    • Article 16 MR2170432
    • Purdom, E. and Holmes, S. P. (2005) Error Distribution for Gene Expression Data. SAGMB 4(1), Article 16 MR2170432
    • (2005) SAGMB , vol.4 , Issue.1
    • Purdom, E.1    Holmes, S.P.2
  • 36
    • 75249091594 scopus 로고    scopus 로고
    • Optimal weighting for false discovery rate control
    • MR2521216
    • Roquain, E., and van de Wiel, M. A. (2009). Optimal weighting for false discovery rate control. Electronic Journal of Statistics 3, 678-711. MR2521216
    • (2009) Electronic Journal of Statistics , vol.3 , pp. 678-711
    • Roquain, E.1    van de Wiel, M.A.2
  • 37
    • 0000120766 scopus 로고
    • Estimating the Dimension of a Model
    • MR0468014
    • Schwarz, G. (1978). Estimating the Dimension of a Model. Ann. Statist. 6(2), 461-464. MR0468014
    • (1978) Ann. Statist. , vol.6 , Issue.2 , pp. 461-464
    • Schwarz, G.1
  • 38
    • 33644910161 scopus 로고    scopus 로고
    • An exploration of aspects of Bayesian multiple testing
    • MR2235051
    • Scott, J. G. and Berger, J. O. (2006). An exploration of aspects of Bayesian multiple testing. J. Statist. Plann. Inference 136(7), 2144-2162. MR2235051
    • (2006) J. Statist. Plann. Inference , vol.136 , Issue.7 , pp. 2144-2162
    • Scott, J.G.1    Berger, J.O.2
  • 40
    • 0345822598 scopus 로고    scopus 로고
    • The positive false discovery rate: A Bayesian interpretation and the q-value
    • MR2036398
    • Storey, J. D. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value. Ann. Statist., 31(6), 2013-2035. MR2036398
    • (2003) Ann. Statist. , vol.31 , Issue.6 , pp. 2013-2035
    • Storey, J.D.1
  • 41
    • 34249111910 scopus 로고    scopus 로고
    • The optimal discovery procedure: A new approach to simultaneous significance testing
    • MR2323757
    • Storey, J. D. (2007). The optimal discovery procedure: a new approach to simultaneous significance testing. J. R. Statist. Soc. B 69, 347-368. MR2323757
    • (2007) J. R. Statist. Soc. B , vol.69 , pp. 347-368
    • Storey, J.D.1
  • 42
    • 35348872772 scopus 로고    scopus 로고
    • Oracle and adaptive compound decision rules for false discovery rate control
    • MR2411657
    • Sun, W. and Cai, T. C. (2007). Oracle and adaptive compound decision rules for false discovery rate control. J. Amer. Statist. Assoc. 102, 901-912. MR2411657
    • (2007) J. Amer. Statist. Assoc. , vol.102 , pp. 901-912
    • Sun, W.1    Cai, T.C.2
  • 43
    • 85194972808 scopus 로고    scopus 로고
    • Regression Shrinkage and Selection via the Lasso
    • MR1379242
    • Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. J. R. Stat. Soc. Ser. B, 58, 267-288. MR1379242
    • (1996) J. R. Stat. Soc. Ser. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 44
    • 79959704858 scopus 로고    scopus 로고
    • Modified versions of Bayesian Information Criterion for sparse Generalized LinearModels
    • MR2813055
    • Zak-Szatkowska, M. and Bogdan, M. (2011). Modified versions of Bayesian Information Criterion for sparse Generalized LinearModels, Comput. Stat. Data An. 55, 2908-2924. MR2813055
    • (2011) Comput. Stat. Data An. , vol.55 , pp. 2908-2924
    • Zak-Szatkowska, M.1    Bogdan, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.