Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 26, 1997 - Issue 11
Submit an article Journal homepage
65
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

General saddlepoint approximations and normalizing transformations for multivariate statistics

Takahiro Tsuchiya The Institute of Statistical Mathematics, Tokyo, Minami-Azabu, Minato-ku, 106, Japan
&
Sadanori Konishi The Institute of Statistical Mathematics, Tokyo, Minami-Azabu, Minato-ku, 106, Japan
Pages 2541-2563 | Received 01 Aug 1997, Published online: 27 Jun 2007

References

  • Bhattacharya , R. N. and Ghosh , J. K. 1978 . On the validity of the formal Edgeworth expansion . Ann. Statist , : 6 434 – 451 .
  • Daniels , H. E. 1954 . Saddlepoint approximations in statistics . Ann. Math. Statist. , 25 : 631 – 650 .
  • David , F. N. 1938 . Tables of the Ordinates and Probability Integral of the Distribution of the Correlation Coefficient in Small Samples. , Cambridge Univ. Press .
  • Easton , G. S. and Ronchetti , E. 1986 . General saddlepoint approximationswith applications to L statistics . J. Amer. Statist. Ass , 81 : 420 – 430 .
  • Field , C. A. and Ronchetti , E. 1990 . Small Sample Asymptotics . IMS Lec¬ture Notes , 13
  • Harvill , J. L. and Newton , H. J. 1995 . Saddlepoint approximations for the difference of order statistics . Biometrika , 82 : 226 – 231 .
  • Konishi , S. 1981 . Normalizing transformations of some statistics in multi¬variate analysis . Biometrika , 68 : 647 – 651 .
  • Konishi , S. 1987 . Transformations of statistics in multivariate analysis . In Advances in Multivariate Statistical Analysis , 68 : 213 – 231 .
  • Lugannani , R. and Rice , S. 1987 . Saddlepoint approximation for the distri¬bution of the sum of independent random variables . Adv. Appl. Prob , 12 : 475 – 490 .
  • Niki , N. and Konishi , S. 1986 . Effects of transformations in higher order asymptotic expansions . Ann. Inst. Statist. Math , 38A : 371 – 383 .
  • Reid , N. 1988 . Saddlepoint methods and statistical inference . Statist. Sci , 3 : 213 – 238 .
  • Sugiura , N. 1973 . Derivatives of the characteristic root of a symmetric or a Hermitian matrix with two applications in multivariate analysis . Com-mun. Statist. , 1 : 393 – 417 .
  • Sugiura , N. 1976 . Asymptotic expansions of the distributions of the canon¬ical correlations. In Commemoration Volume of the Founding of the Faculty of Integrated Arts and Sciences . Hiroshima University , 1 : 141 – 163 .
  • Wang , S. 1992 . General saddlepoint approximations in the bootstrap . Statist. Prob. Letters , 13 : 61 – 66 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.