메뉴 건너뛰기




Volumn 13, Issue 2, 2007, Pages 346-364

Limiting distributions of the non-central t-statistic and their applications to the power of t-tests under non-normality

Author keywords

Domain of attraction; Limit theorems; Non central t statistic; Power of t test

Indexed keywords


EID: 40249117671     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ5073     Document Type: Article
Times cited : (15)

References (28)
  • 1
    • 12344256249 scopus 로고
    • A higher order approximation to a percentage point of the non-central t-distribution
    • Akahira, M. (1995) A higher order approximation to a percentage point of the non-central t-distribution. Comm. Statist. Simul. Comput., 24, 595-605.
    • (1995) Comm. Statist. Simul. Comput , vol.24 , pp. 595-605
    • Akahira, M.1
  • 3
    • 21344464403 scopus 로고    scopus 로고
    • Bentkus, V, Bloznelis, M. and Götze, E (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, E (1996) A Berry-Esséen bound for Student's statistic in the non-i.i.d. case. J. Theoret. Probab., 9, 765-796.
  • 4
    • 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
  • 5
    • 0032264526 scopus 로고    scopus 로고
    • The sample autocorrelations of heavy-tailed processes with applications to ARCH
    • Davis, R.A. and Mikosch, T. (1998) The sample autocorrelations of heavy-tailed processes with applications to ARCH. Ann. Statist., 26, 2049-2080.
    • (1998) Ann. Statist , vol.26 , pp. 2049-2080
    • Davis, R.A.1    Mikosch, T.2
  • 7
    • 0039378037 scopus 로고    scopus 로고
    • When is the Student t-statistic asymptotically standard normal?
    • Giné, E., Götze, F. and Mason, D.M. (1997) When is the Student t-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.M.3
  • 8
    • 3042562278 scopus 로고    scopus 로고
    • Tightness of the Student t-statistic
    • Griffin, P.S. (2002) Tightness of the Student t-statistic. Electron. Comm. Probab., 7, 181-190.
    • (2002) Electron. Comm. Probab , vol.7 , pp. 181-190
    • Griffin, P.S.1
  • 10
    • 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
  • 11
    • 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., 32, 2679-2711.
    • (2004) Ann. Statist , vol.32 , pp. 2679-2711
    • Jing, B.-Y.1    Shao, Q.-M.2    Zhou, W.3
  • 12
    • 0000880505 scopus 로고
    • Applications of the non-central t-distribution
    • Johnson, N.L. and Welch, B.L. (1940) Applications of the non-central t-distribution. Biometrika, 31, 362-389.
    • (1940) Biometrika , vol.31 , pp. 362-389
    • Johnson, N.L.1    Welch, B.L.2
  • 14
    • 33744810886 scopus 로고    scopus 로고
    • Stable limits of martingale transforms with application to the estimation of GARCH parameters
    • Mikosch, T. and Straumann, D. (2006) Stable limits of martingale transforms with application to the estimation of GARCH parameters. Ann. Statisit., 34, 493-522.
    • (2006) Ann. Statisit , vol.34 , pp. 493-522
    • Mikosch, T.1    Straumann, D.2
  • 15
    • 0001697508 scopus 로고
    • Statistical problems in agricultural experimentation
    • Neyman, J. (1935) Statistical problems in agricultural experimentation. J. Roy. Statist. Soc. Ser B, Suppl. 2, 107.
    • (1935) J. Roy. Statist. Soc. Ser B , vol.2 , Issue.SUPPL. , pp. 107
    • Neyman, J.1
  • 16
    • 0344139871 scopus 로고
    • Errors of the second kind in testing 'Student's' hypothesis
    • Neyman, J. and Tokarska, B. (1936) Errors of the second kind in testing 'Student's' hypothesis. J. Amer. Statist. Assoc., 31, 318-326.
    • (1936) J. Amer. Statist. Assoc , vol.31 , pp. 318-326
    • Neyman, J.1    Tokarska, B.2
  • 17
    • 0006075504 scopus 로고
    • A special case of a bivariate non-central t-distribution
    • Owen, D.B. (1965) A special case of a bivariate non-central t-distribution. Biometrika, 52, 437-446.
    • (1965) Biometrika , vol.52 , pp. 437-446
    • Owen, D.B.1
  • 19
    • 0000616908 scopus 로고
    • A bivariate stable characterization and domains of attraction
    • Resnick, S. and Greenwood, P. (1979) A bivariate stable characterization and domains of attraction. J Multivariate Anal., 9, 206-221.
    • (1979) J Multivariate Anal , vol.9 , pp. 206-221
    • Resnick, S.1    Greenwood, P.2
  • 21
    • 34248977147 scopus 로고
    • Some percentage points of the non-central t-distribution
    • Scheuer, E.M. and Spurgeon, R.A. (1963) Some percentage points of the non-central t-distribution. J. Amer Statist. Assoc., 58, 176-182.
    • (1963) J. Amer Statist. Assoc , vol.58 , pp. 176-182
    • Scheuer, E.M.1    Spurgeon, R.A.2
  • 23
    • 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
  • 24
    • 0033441791 scopus 로고    scopus 로고
    • A Cramér type large deviation result for Student's t-statistic
    • Shao, Q.-M. (1999) A Cramér 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
  • 25
    • 0011593147 scopus 로고
    • Effect of non-normality on the power function of t-test
    • Srivastava, A.B.L. (1958) Effect of non-normality on the power function of t-test. Biometrika, 45, 421-430.
    • (1958) Biometrika , vol.45 , pp. 421-430
    • Srivastava, A.B.L.1
  • 26
    • 0043158967 scopus 로고    scopus 로고
    • Hypothesis testing for the generalized multivariate modified Bessel model
    • Thabane, L. and Drekic, S. (2003) Hypothesis testing for the generalized multivariate modified Bessel model. J. Multivariate Anal., 86, 360-374.
    • (2003) J. Multivariate Anal , vol.86 , pp. 360-374
    • Thabane, L.1    Drekic, S.2
  • 27
    • 47249143929 scopus 로고
    • On the use of the non-central t-distribution for comparing percentage points of normal populations
    • Walsh, J.E. (1948) On the use of the non-central t-distribution for comparing percentage points of normal populations. Ann. Math. Statist., 19, 93-94.
    • (1948) Ann. Math. Statist , vol.19 , pp. 93-94
    • Walsh, J.E.1
  • 28
    • 0033212383 scopus 로고    scopus 로고
    • An exponential non-uniform Berry-Esséen bound for self-normalized sums
    • Wang, Q.Y. and Jing, B.-Y. (1999) An exponential non-uniform Berry-Esséen bound for self-normalized sums. Ann. Probab., 27, 2068-2088.
    • (1999) Ann. Probab , vol.27 , pp. 2068-2088
    • Wang, Q.Y.1    Jing, B.-Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.