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Volumn 19, Issue 1, 2009, Pages 343-354

Relative errors in central limit theorems for student's t statistic, with applications

Author keywords

Classification; Family wise error rate; Genomics; Large deviation expansion; Signal detection; Simultaneous hypothesis testing; Sparsity

Indexed keywords


EID: 64549101616     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (17)

References (34)
  • 1
    • 21344464403 scopus 로고    scopus 로고
    • Bentkus, V., Bloznelis, M. and Götze, F. (1996). A Berry-Esséen bound for Student's statistic in the non-i.i.d. case. J. Theoret. Probab. 9, 765-796.
    • Bentkus, V., Bloznelis, M. and Götze, F. (1996). A Berry-Esséen bound for Student's statistic in the non-i.i.d. case. J. Theoret. Probab. 9, 765-796.
  • 2
    • 0038877700 scopus 로고    scopus 로고
    • The Berry-Esseen bound for Student's statistic
    • Bentkus, V. and Götze, F. (1996). The Berry-Esseen bound for Student's statistic. Ann. Probab. 24, 491-503.
    • (1996) Ann. Probab , vol.24 , pp. 491-503
    • Bentkus, V.1    Götze, F.2
  • 3
    • 0040644411 scopus 로고    scopus 로고
    • An Edgeworth expansion for symmetric statistics
    • Bentkus, V., Götze, F. and VAN Zwet, W.R. (1997). An Edgeworth expansion for symmetric statistics. Ann. Statist. 25, 851-896.
    • (1997) Ann. Statist , vol.25 , pp. 851-896
    • Bentkus, V.1    Götze, F.2    VAN Zwet, W.R.3
  • 4
    • 40249117671 scopus 로고    scopus 로고
    • Limit distributions of non-central t-statistic and their applications to the power of t-test under non-normality
    • Bentkus, V., Jing, B.-Y., Shao, Q.-M. and Zhou, W. (2007). Limit distributions of non-central t-statistic and their applications to the power of t-test under non-normality. Bernoulli 13, 346-364.
    • (2007) Bernoulli , vol.13 , pp. 346-364
    • Bentkus, V.1    Jing, B.-Y.2    Shao, Q.-M.3    Zhou, W.4
  • 5
    • 64549150400 scopus 로고    scopus 로고
    • Bloznelis, M. and Putter, H. (1998). One term Edgeworth expansion for Student's t statistic. Probability Theory and Mathematical Statistics: Proceedings of the Seventh Vilnius Conference. (Edited by B. Grigelionis et al.), 81-98. Vilnius, Utrecht: VSP/TEV.
    • Bloznelis, M. and Putter, H. (1998). One term Edgeworth expansion for Student's t statistic. Probability Theory and Mathematical Statistics: Proceedings of the Seventh Vilnius Conference. (Edited by B. Grigelionis et al.), 81-98. Vilnius, Utrecht: VSP/TEV.
  • 6
    • 0038472171 scopus 로고    scopus 로고
    • Second Order and Bootstrap Approximation to Student's Statistic
    • Bloznelis, M. and Putter, H. (2002). Second Order and Bootstrap Approximation to Student's Statistic. Theory Probab. Appl. 47, 374-381.
    • (2002) Theory Probab. Appl , vol.47 , pp. 374-381
    • Bloznelis, M.1    Putter, H.2
  • 7
    • 3042566735 scopus 로고
    • Asymptotic expansion for the distribution of statistics admitting a stochastic expansion. I
    • Chibisov, D. M. (1980). Asymptotic expansion for the distribution of statistics admitting a stochastic expansion. I. Teor. Veroyatnost. i Primenen. 25, 745-756.
    • (1980) Teor. Veroyatnost. i Primenen , vol.25 , pp. 745-756
    • Chibisov, D.M.1
  • 8
    • 0040899490 scopus 로고
    • Asymptotic expansions and deficiencies of tests
    • Edited by Z. Ciesielski and C. Olech, PWN, Warsaw
    • Chibisov, D. M. (1984). Asymptotic expansions and deficiencies of tests. In: Proceedings of the International Congress of Mathematicians 1 (Edited by Z. Ciesielski and C. Olech), 1063-1079. PWN, Warsaw.
    • (1984) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 1063-1079
    • Chibisov, D.M.1
  • 9
    • 2142651769 scopus 로고    scopus 로고
    • Limit distributions of Studentized means
    • Chistyakov, G. P. and Götze, F. (2004). Limit distributions of Studentized means. Ann. Probab. 32, 28-77.
    • (2004) Ann. Probab , vol.32 , pp. 28-77
    • Chistyakov, G.P.1    Götze, F.2
  • 10
    • 38349004114 scopus 로고    scopus 로고
    • Robustness of multiple testing procedures against dependence
    • Manuscript
    • Clarke, S. and Hall, P. (2007). Robustness of multiple testing procedures against dependence. Manuscript.
    • (2007)
    • Clarke, S.1    Hall, P.2
  • 11
    • 0038711284 scopus 로고    scopus 로고
    • Donsker's theorem for self-normalized partial sums processes
    • Csörhö, M., Szyszkowicz, B. and Wang, Q. (2003). Donsker's theorem for self-normalized partial sums processes. Ann. Probab. 31, 1228-1240.
    • (2003) Ann. Probab , vol.31 , pp. 1228-1240
    • Csörhö, M.1    Szyszkowicz, B.2    Wang, Q.3
  • 12
    • 33749667892 scopus 로고    scopus 로고
    • On weighted approximations and strong limit theorems for self-normalized partial sums processes
    • Fields Inst. Commun. 44, Amer. Math. Soc, Providence, RI
    • Csörhö, M., Szyszkowicz, B. and Wang, Q. (2004). On weighted approximations and strong limit theorems for self-normalized partial sums processes. In Asymptotic methods in Stochastics, 489-521. Fields Inst. Commun. 44, Amer. Math. Soc., Providence, RI.
    • (2004) Asymptotic methods in Stochastics , pp. 489-521
    • Csörhö, M.1    Szyszkowicz, B.2    Wang, Q.3
  • 13
    • 50649095626 scopus 로고    scopus 로고
    • Using threshold methods to extend higher-criticism classification to non-normal, dependent vector components
    • Manuscript
    • Delaigle, A. and Hall, P. (2007). Using threshold methods to extend higher-criticism classification to non-normal, dependent vector components. Manuscript.
    • (2007)
    • Delaigle, A.1    Hall, P.2
  • 14
    • 23744475601 scopus 로고    scopus 로고
    • Higher criticism for detecting sparse heterogeneous mixtures
    • Donoho, D. L. and Jin, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32, 962-994.
    • (2004) Ann. Statist , vol.32 , pp. 962-994
    • Donoho, D.L.1    Jin, J.2
  • 15
    • 0001161575 scopus 로고
    • A Berry-Esseen bound for functions of independent random variables
    • Friedrich, K. O. (1989). A Berry-Esseen bound for functions of independent random variables. Ann. Statist. 17, 170-183.
    • (1989) Ann. Statist , vol.17 , pp. 170-183
    • Friedrich, K.O.1
  • 16
    • 0039378037 scopus 로고    scopus 로고
    • When is the Student ť-statistic asymptotically standard normal?
    • Giné, E., Götze, F. and Mason, D. (1997). When is the Student ť-statistic asymptotically standard normal? Ann. Probab. 25, 1514-1531.
    • (1997) Ann. Probab , vol.25 , pp. 1514-1531
    • Giné, E.1    Götze, F.2    Mason, D.3
  • 17
    • 0000658406 scopus 로고
    • Edgeworth expansion for Student's t statistic under minimal moment conditions
    • Hall, P. (1987). Edgeworth expansion for Student's t statistic under minimal moment conditions. Ann. Probab. 15, 920-931.
    • (1987) Ann. Probab , vol.15 , pp. 920-931
    • Hall, P.1
  • 18
    • 84869269458 scopus 로고    scopus 로고
    • Some contemporary problems in statistical science
    • Edited by F. Chamizo and A. Quirós, Springer, New York
    • Hall, P. (2006). Some contemporary problems in statistical science. In Madrid Intelligencer (Edited by F. Chamizo and A. Quirós), 38-41. Springer, New York.
    • (2006) Madrid Intelligencer , pp. 38-41
    • Hall, P.1
  • 19
    • 3042633756 scopus 로고    scopus 로고
    • Exact convergence rate and leading term in central limit theorem for student's t statistic
    • Hall, P. and Wang, Q. (2004). Exact convergence rate and leading term in central limit theorem for student's t statistic. Ann. Probab. 32, 1419-1437.
    • (2004) Ann. Probab , vol.32 , pp. 1419-1437
    • Hall, P.1    Wang, Q.2
  • 20
    • 0346961351 scopus 로고    scopus 로고
    • Self-normalized Cramér-type large deviations for independent random variables
    • Jing, B.-Y., Shao, Q.-M. and Wang, Q. (2003). Self-normalized Cramér-type large deviations for independent random variables. Ann. Probab. 31, 2167-2215.
    • (2003) Ann. Probab , vol.31 , pp. 2167-2215
    • Jing, B.-Y.1    Shao, Q.-M.2    Wang, Q.3
  • 21
    • 21644471134 scopus 로고    scopus 로고
    • Saddlepoint approximation for Student's t-statistic with no moment conditions
    • Jing, B.-Y., Shao, Q.-M. and Zhou, W. (2004). Saddlepoint approximation for Student's t-statistic with no moment conditions. Ann. Statist. 6, 2679-2711.
    • (2004) Ann. Statist , vol.6 , pp. 2679-2711
    • Jing, B.-Y.1    Shao, Q.-M.2    Zhou, W.3
  • 22
  • 23
    • 26044476911 scopus 로고    scopus 로고
    • The asymptotic distribution of self-normalized triangular arrys
    • Mason, D. M. (2005). The asymptotic distribution of self-normalized triangular arrys. J. Theoret. Probab. 18, 853-870.
    • (2005) J. Theoret. Probab , vol.18 , pp. 853-870
    • Mason, D.M.1
  • 24
    • 0041171600 scopus 로고    scopus 로고
    • Empirical Edgeworth expansions for symmetric statistics
    • Putter, H. and VAN Zwet, H. R. (1998). Empirical Edgeworth expansions for symmetric statistics. Ann. Statist. 26, 1540-1569.
    • (1998) Ann. Statist , vol.26 , pp. 1540-1569
    • Putter, H.1    VAN Zwet, H.R.2
  • 26
    • 26044453588 scopus 로고    scopus 로고
    • On the self-normalized Cramér-type large deviation
    • Robinson, J. and Wang, Q. (2005). On the self-normalized Cramér-type large deviation. J. Theoret. Probab. 18, 891-909.
    • (2005) J. Theoret. Probab , vol.18 , pp. 891-909
    • Robinson, J.1    Wang, Q.2
  • 27
    • 0031531828 scopus 로고    scopus 로고
    • Self-normalized large deviations
    • Shao, Q.-M. (1997). Self-normalized large deviations. Ann. Probab. 25, 285-328.
    • (1997) Ann. Probab , vol.25 , pp. 285-328
    • Shao, Q.-M.1
  • 28
    • 0033441791 scopus 로고    scopus 로고
    • A Cramer type large deviation result for Student's t-statistic
    • Shao, Q.-M. (1999). A Cramer type large deviation result for Student's t-statistic. J. Theoret. Probab. 12, 385-398.
    • (1999) J. Theoret. Probab , vol.12 , pp. 385-398
    • Shao, Q.-M.1
  • 29
    • 0001378132 scopus 로고
    • On the Berry-Esseen bound for Student's statistic
    • Stability Problems for Stochastic Models, Edited by V. V. Kalashnikov and V. M. Zolotarev, Springer, Berlin
    • Slavov, V. V. (1985). On the Berry-Esseen bound for Student's statistic. In: Stability Problems for Stochastic Models, (Edited by V. V. Kalashnikov and V. M. Zolotarev) Lecture Notes in Math. 1155, 355-390. Springer, Berlin.
    • (1985) Lecture Notes in Math , vol.1155 , pp. 355-390
    • Slavov, V.V.1
  • 30
    • 0000654995 scopus 로고
    • A Berry-Esseen bound for symmetric statistics
    • VAN Zwet, W. R. (1984). A Berry-Esseen bound for symmetric statistics. Z. Wahrsch. Verw. Gebiete 66, 425-440.
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.66 , pp. 425-440
    • VAN Zwet, W.R.1
  • 31
    • 27844456474 scopus 로고    scopus 로고
    • Limit Theorems for self-normalized large deviation
    • Wang, Q. (2005). Limit Theorems for self-normalized large deviation. Electronic J. Probab. 10, 1260-1285.
    • (2005) Electronic J. Probab , vol.10 , pp. 1260-1285
    • Wang, Q.1
  • 32
    • 0033212383 scopus 로고    scopus 로고
    • An exponential nonuniform Berry-Esseen bound for self-normalized sums
    • Wang, Q. and Jing, B.-Y. (1999). An exponential nonuniform Berry-Esseen bound for self-normalized sums. Ann. Probab. 27, 2068-2088.
    • (1999) Ann. Probab , vol.27 , pp. 2068-2088
    • Wang, Q.1    Jing, B.-Y.2
  • 33
    • 0033630625 scopus 로고    scopus 로고
    • The Berry-Esseen bound for Studentized statistics
    • Wang, Q., Jing, B.-Y. and Zhao, L. C. (2000). The Berry-Esseen bound for Studentized statistics. Ann. Probab. 28, 511-535.
    • (2000) Ann. Probab , vol.28 , pp. 511-535
    • Wang, Q.1    Jing, B.-Y.2    Zhao, L.C.3
  • 34
    • 33749007440 scopus 로고    scopus 로고
    • Tail probability approximations for Student's t statistics
    • Zhou, W. and Jing, B.-Y. (2006). Tail probability approximations for Student's t statistics. Probab. Theory Relat. Fields, 136, 541-559.
    • (2006) Probab. Theory Relat. Fields , vol.136 , pp. 541-559
    • Zhou, W.1    Jing, B.-Y.2


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