Saddlepoint approximation for student's t-statistic with no moment conditions

Annals of Statistics

Volumn 32, Issue 6, 2004, Pages 2679-2711

  Jing, Bing Yi ^a,b,c   Shao, Qi Man ^b,c   Zhou, Wang ^c  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b UNIVERSITY OF OREGON   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Absolute error; Asymptotic normality; Edgeworth expansion; Large deviation; Relative error; Saddlepoint approximation; Self normalized sum; Student's t statistic

Indexed keywords

EID: 21644471134     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000000742     Document Type: Article

References (16)

1. DANIELS, H. E. and YOUNG, G. A. (1991). Saddlepoint approximation for the Studentized mean, with an application to the bootstrap. Biomelrika 78 169-179.
2. DAVISON, A. C. and HINKLEY, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Univ. Press.
3. DEMBO, A. and SHAO, Q.-M. (1998). Self-normalized large deviations in vector spaces. In High-Dimensional Probability (E. Eberlein, M. Hahn and M. Talagrand, eds.) 27-32. Birkhäuser, Basel.
4. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York.
5. FIELD, C. and RONCHETTI, E. (1990). Small Sample Asymptotics. IMS, Hayward, CA.
6. GINÉ, E., GÖTZE, F. and MASON, D. M. (1997). When is the Student t-statistic asymptotically standard normal? Ann. Probab. 25 1514-1531.
7. GRIFFIN, P. S. and KUELBS, J. (1989). Self-normalized laws of the iterated logarithm. Ann. Probab. 17 1571-1601.
8. GRIFFIN, P. S. and KUELBS, J. (1991). Some extensions of the LIL via self-normalizations. Ann. Probab. 19 380-395.
9. HALL, P. (1987). Edgeworth expansion for Student's t statistic under minimal moment conditions. Ann. Probab. 15 920-931.
10. JENSEN, J. L. (1995). Saddlepoint Approximations. Oxford Univ. Press.
11. KOLASSA, J. E. (1997). Series Approximation Methods in Statistics, 2nd ed. Lecture Notes in Statist. 88. Springer, New York.
12. LOGAN, B. F., MALLOWS, C. L., RICE, S. O. and SHEPP, L. A. (1973). Limit distributions of self-normalized sums. Ann. Probab. 1 788-809.
13. LUGANNANI, R. and RICE, S. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables. Adv. in Appl. Probab. 12 475-490.
14. REID, N. (1988). Saddlepoint methods and statistical inference (with discussion). Statist. Sci. 3 213-238.
15. SHAO, Q.-M. (1997) Self-normalized large deviations. Ann. Probab. 25 285-328.
16. WANG, Q. Y. and JING, B.-Y. (1999). An exponential nonuniform Berry-Esseen bound for self-normalized sums. Ann. Probab. 27 2068-2088.