High-Dimensional Inference and False Discovery

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)


False Discovery Rate Asymptotic Expansion Likelihood Ratio Statistic Detection Boundary High Criticism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramovich, F., Benjamini, Y., Donoho, D., and Johnstone, I. (2006). Adapting to unknown sparsity by controlling the FDR, Ann. Stat., 34, 584–653.MATHCrossRefMathSciNetGoogle Scholar
  2. Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing, J.R. Stat. Soc. B, 57, 289–300.MATHMathSciNetGoogle Scholar
  3. Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency, Ann. Stat., 29, 1165–1188.MATHCrossRefMathSciNetGoogle Scholar
  4. Bernhard, G., Klein, M., and Hommel, G. (2004). Global and multiple test procedures using ordered P-values—a review, Stat. Papers, 45, 1–14.MATHCrossRefMathSciNetGoogle Scholar
  5. Bickel, P. and Levina, E. (2004). Some theory of Fisher’s linear discriminant function, ‘naive Bayes’, and some alternatives when there are many more variables than observations, Bernoulli, 10, 989–1010.MATHMathSciNetCrossRefGoogle Scholar
  6. Birnbaum, Z. and Pyke, R. (1958). On some distributions related to the statistic D_n+, Ann. Math. Stat., 29, 179–187.CrossRefMathSciNetMATHGoogle Scholar
  7. Brown, L. (1979). A proof that the Tukey-Kramer multiple comparison procedure is level α for 3, 4, or 5 treatments, Technical Report, Cornell University.Google Scholar
  8. Brown, L. (1984). A note on the Tukey-Kramer procedure for pairwise comparison of correlated means, in Design of Experiments: Ranking and Selection, T.J. Santner and A. Tamhane (eds.), Marcel Dekker, New York, 1–6.Google Scholar
  9. Chang, C., Rom, D., and Sarkar, S. (1996). A modified Bonferroni procedure for repeated significance testing, Technical Report, Temple University.Google Scholar
  10. DasGupta, A. and Zhang, T. (2006). On the false discovery rates of a frequentist: asymptotic expansions, Lecture Notes and Monograph Series, Vol. 50, Institute of Mathematical Statistics, Beachwood, OH, 190–212.Google Scholar
  11. Delaigle, A. and Hall, P. (2006). Using thresholding methods to extend higher criticism classification to non-normal dependent vector components, manuscript.Google Scholar
  12. Dempster, A. (1959). Generalized D_n+ statistic, Ann. Math. Stat., 30, 593–597.MathSciNetMATHGoogle Scholar
  13. Donoho, D. and Jin, J. (2004). Higher criticism for detecting sparse heterogenous mixtures, Ann. Stat., 32, 962–994.MATHCrossRefMathSciNetGoogle Scholar
  14. Donoho, D. and Jin, J. (2006). Asymptotic minimaxity of FDR thresholding for sparse Exponential data, Ann. Stat., 34, 2980–3018.MATHCrossRefMathSciNetGoogle Scholar
  15. Efron, B. (2003). Robbins, Empirical Bayes, and microarrays, Ann. Stat., 31, 366–378.MATHCrossRefMathSciNetGoogle Scholar
  16. Efron, B. (2007). Correlation and large scale simultaneous significance testing, J. Am. Stat. Assoc., 102, 93–103.MATHCrossRefMathSciNetGoogle Scholar
  17. Efron, B., Tibshirani, R., Storey, J. and Tusher, V. (2001). Empirical Bayes analysis of a microarray experiment, J. Am. Stat. Assoc., 96, 1151–1160.MATHCrossRefMathSciNetGoogle Scholar
  18. Finner, H. and Roters, M. (2002). Multiple hypothesis testing and expected number of type I errors, Ann. Stat., 30, 220–238.Google Scholar
  19. Genovese, C. and Wasserman, L. (2002). Operating characteristics and extensions of the false discovery rate procedure, J. R. Stat. Soc. B, 64, 499–517.MATHCrossRefMathSciNetGoogle Scholar
  20. Genovese, C. and Wasserman, L. (2004). A stochastic process approach to false discovery control, Ann. Stat., 32, 1035–1061.MATHCrossRefMathSciNetGoogle Scholar
  21. Genovese, C., Roeder, K. and Wasserman, L. (2006). False discovery control with P-value weighting, Biometrika, 93, 509–524.MATHCrossRefMathSciNetGoogle Scholar
  22. Hall, P. and Jin, J. (2007). Performance of higher criticism under strong dependence (in press).Google Scholar
  23. Hayter, A. (1984). A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative, Ann. Stat., 12, 61–75.MATHCrossRefMathSciNetGoogle Scholar
  24. Hochberg, Y. and Tamhane, A. (1987). Multiple Comparisons Procedures, John Wiley, New York.Google Scholar
  25. Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance, Biometrika, 75, 800–803.MATHCrossRefMathSciNetGoogle Scholar
  26. Holst, L. (1972). Asymptotic normality and efficiency for certain goodness of fit tests, Biometrika, 59, 137–145.MATHCrossRefMathSciNetGoogle Scholar
  27. Hommel, G. (1988). A stage-wise rejective multiple test procedure based on a modified Bonferroni test, Biometrika, 75, 383–386.MATHCrossRefGoogle Scholar
  28. Huber, P. (1973). Robust regression: asymptotics, conjectures, and Monte Carlo, Ann. Stat., 1, 799–821.MATHCrossRefMathSciNetGoogle Scholar
  29. Karlin, S. and Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities I: multivariate totally positive distributions, J. Multivar. Anal., 10, 467–498.MATHCrossRefMathSciNetGoogle Scholar
  30. Koehler, K. and Larntz, K. (1980). An empirical investigation of goodness of fit statistics for sparse multinomials, J. Am. Stat. Assoc., 75, 336–344.Google Scholar
  31. Kramer, C. (1956). Extension of multiple range tests to group means with unequal numbers of replications, Biometrics, 12, 307–310.CrossRefMathSciNetGoogle Scholar
  32. Meinshausen, M. and Bühlmann, P. (2005). Lower bounds for the number of false null hypotheses for multiple testing of association under general dependence structures, Biometrika, 92, 893–907.CrossRefMathSciNetMATHGoogle Scholar
  33. Meinshausen, M. and Rice, J. (2006). Estimating the proportion of false null hypotheses among a large number of independent hypotheses, Ann. Stat., 34, 373–393.MATHCrossRefMathSciNetGoogle Scholar
  34. Miller, R. (1966). Simultaneous Statistical Inference, McGraw-Hill, New York.MATHGoogle Scholar
  35. Morris, C. (1975). Central limit theorems for multinomial sums, Ann. Stat., 3, 165–188.CrossRefGoogle Scholar
  36. Portnoy, S. (1984). Asymptotic behavior of M-estimates of p regression parameters when p^2/n is large I: consistency, Ann. Stat., 12, 1298–1309.MATHCrossRefMathSciNetGoogle Scholar
  37. Portnoy, S. (1985). Asymptotic behavior of M-estimates of p regression parameters when p^2/n is large II: normal approximation, Ann. Stat., 13, 1403–1417.MATHCrossRefMathSciNetGoogle Scholar
  38. Portnoy, S. (1988). Asymptotic behavior of likelihood methods for Exponential families when the number of parameters tends to infinity, Ann. Stat., 16, 356–366.MATHCrossRefMathSciNetGoogle Scholar
  39. Sarkar, S. and Chang, C. (1997). The Simes method for multiple hypotheses testing with positively dependent test statistics, J. Am. Stat. Assoc., 92, 1601–1608.MATHCrossRefMathSciNetGoogle Scholar
  40. Sarkar, S. (2006). False discovery and false nondiscovery rates in single step multiple testing procedures, Ann. Stat., 34, 394–415.MATHCrossRefMathSciNetGoogle Scholar
  41. Scott, J. and Berger, J. (2006). An exploration of aspects of Bayesian multiple testing, J. Stat. Planning Infer, 136, 2144–2162.MATHCrossRefMathSciNetGoogle Scholar
  42. Seo, T., Mano, S., and Fujikoshi, Y. (1994). A generalized Tukey conjecture for multiple comparison among mean vectors, J. Am. Stat. Assoc., 89, 676–679.MATHCrossRefMathSciNetGoogle Scholar
  43. Shaffer, J. (1995). Multiple hypothesis testing: a review, Annu. Rev. Psychol., 46, 561–584.CrossRefGoogle Scholar
  44. Simes, R. (1986). An improved Bonferroni procedure for multiple tests of significance, Biometrika, 73, 751–754.MATHCrossRefMathSciNetGoogle Scholar
  45. Sólric, B. (1989). Statistical ‘discoveries’ and effect-size estimation, J. Am. Stat. Assoc., 84, 608–610.CrossRefGoogle Scholar
  46. Storey, J. (2002). A direct approach to false discovery rates, J. R. Stat. Soc. B, 64, 479–498.MATHCrossRefMathSciNetGoogle Scholar
  47. Storey, J. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value, Ann. Stat., 31, 2013–2035.MATHCrossRefMathSciNetGoogle Scholar
  48. Storey, J. and Tibshirani, R. (2003). Statistical significance for genomewide studies, Proc. Natl. Acad. Sci. USA, 16, 9440–9445.CrossRefMathSciNetGoogle Scholar
  49. Storey, J., Taylor, J., and Siegmund, D. (2004). Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach, J. R. Stat. Soc. B, 66, 187–205.MATHCrossRefMathSciNetGoogle Scholar
  50. Sun, W. and Cai, T. (2007). Oracle and adaptive compound decision rules for false discovery rate control, in Press.Google Scholar
  51. Tukey, J. (1953). The problem of multiple comparisons, in The Collected Works of John Tukey, Vol. VIII, Chapman and Hall, New York, 1–300.Google Scholar
  52. Tukey, J. (1991). The philosophy of multiple comparison, Stat. Sci., 6, 100–116.CrossRefGoogle Scholar
  53. Tukey, J. (1993). Where should multiple comparisons go next? In Multiple Comparisons, Selections, and Applications in Biometry, F. Hoppe (ed.), Marcel Dekker, New York.Google Scholar
  54. Westfall, P. and Young, S. (1993). Resampling Based Multiple Testing, John Wiley, New York.Google Scholar
  55. Wright, S. (1992). Adjusted P-values for simultaneous inference, Biometrics, 48, 1005–1013.CrossRefGoogle Scholar
  56. Yohai, V. and Maronna, R. (1979). Asymptotic behavior of M-estimators for the linear model, Ann. Stat., 7, 258–268.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

Personalised recommendations