Advertisement

High-Dimensional Inference and False Discovery

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

Keywords

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramovich, F., Benjamini, Y., Donoho, D., and Johnstone, I. (2006). Adapting to unknown sparsity by controlling the FDR, Ann. Stat., 34, 584–653.zbMATHCrossRefMathSciNetGoogle 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.zbMATHMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHMathSciNetCrossRefGoogle Scholar
  6. Birnbaum, Z. and Pyke, R. (1958). On some distributions related to the statistic D_n+, Ann. Math. Stat., 29, 179–187.CrossRefMathSciNetzbMATHGoogle 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.MathSciNetzbMATHGoogle Scholar
  13. Donoho, D. and Jin, J. (2004). Higher criticism for detecting sparse heterogenous mixtures, Ann. Stat., 32, 962–994.zbMATHCrossRefMathSciNetGoogle Scholar
  14. Donoho, D. and Jin, J. (2006). Asymptotic minimaxity of FDR thresholding for sparse Exponential data, Ann. Stat., 34, 2980–3018.zbMATHCrossRefMathSciNetGoogle Scholar
  15. Efron, B. (2003). Robbins, Empirical Bayes, and microarrays, Ann. Stat., 31, 366–378.zbMATHCrossRefMathSciNetGoogle Scholar
  16. Efron, B. (2007). Correlation and large scale simultaneous significance testing, J. Am. Stat. Assoc., 102, 93–103.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar
  20. Genovese, C. and Wasserman, L. (2004). A stochastic process approach to false discovery control, Ann. Stat., 32, 1035–1061.zbMATHCrossRefMathSciNetGoogle Scholar
  21. Genovese, C., Roeder, K. and Wasserman, L. (2006). False discovery control with P-value weighting, Biometrika, 93, 509–524.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar
  26. Holst, L. (1972). Asymptotic normality and efficiency for certain goodness of fit tests, Biometrika, 59, 137–145.zbMATHCrossRefMathSciNetGoogle Scholar
  27. Hommel, G. (1988). A stage-wise rejective multiple test procedure based on a modified Bonferroni test, Biometrika, 75, 383–386.zbMATHCrossRefGoogle Scholar
  28. Huber, P. (1973). Robust regression: asymptotics, conjectures, and Monte Carlo, Ann. Stat., 1, 799–821.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.CrossRefMathSciNetzbMATHGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar
  34. Miller, R. (1966). Simultaneous Statistical Inference, McGraw-Hill, New York.zbMATHGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar
  40. Sarkar, S. (2006). False discovery and false nondiscovery rates in single step multiple testing procedures, Ann. Stat., 34, 394–415.zbMATHCrossRefMathSciNetGoogle Scholar
  41. Scott, J. and Berger, J. (2006). An exploration of aspects of Bayesian multiple testing, J. Stat. Planning Infer, 136, 2144–2162.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar
  47. Storey, J. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value, Ann. Stat., 31, 2013–2035.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle 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.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

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

Personalised recommendations