When is the student t-statistic asymptotically standard normal?

Annals of Probability

Volumn 25, Issue 3, 1997, Pages 1514-1531

  Giné, Evarist ^a   Götze, Friedrich ^b   Mason, David M ^c  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b BIELEFELD UNIVERSITY   (Germany)

^c UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039378037     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404523     Document Type: Article

References (15)

1. ARAUJO, A. and GINÉ, E. (1980). The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.
2. BENTKUS, V. and GÖTZE, F. (1994). The Berry-Esseen bound for Student's statistic. Ann. Probab. 24 491-503.
3. BREIMAN, L. (1968). Probability. Addison-Wesley, Reading, MA.
4. CSÖRGO, S. (1989). Notes on extreme and self-normalised sums from the domain of attraction of a stable law. J. London Math. Soc. 39 369-384.
5. CSÖRGO, S., HAEUSLER, E. and MASON, D. M. (1988). A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables. Adv. in Appl. Math. 9 259-333.
6. EFRON, B. (1969). Student's t-test under symmetry conditions. J. Amer. Statist. Assoc. 64 1278-1302.
7. FELLER, W. (1966). On regular variation and local limit theorems. In Proc. Fifth Berkeley Symp. Math. Statist. Probab. 2 373-388. Univ. California Press, Berkeley.
8. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2. Wiley, New York.
9. GRIFFIN, P. S. and MASON, D. M. (1991). On the asymptotic normality of self-normalized sums. Proc. Cambridge Phil. Soc. 109 597-610.
10. KAHANE, J.-P. (1968). Some Random Series of Functions. Heath, Lexington, MA.
11. KWAPIEŃ, S. and WOYCZYŃSKI, W. (1992). Random Series and Stochastic Integrals. Birkhäuser, Boston.
12. LEPAGE, R., WOODROOFE, M. and ZINN, J. (1981). Convergence to a stable distribution via order statistics. Ann. Probab. 9 624-632.
13. 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.
14. MALLER, R. A. (1981). A theorem on products of random variables, with application to regression. Austral. J. Statist. 23 177-185.
15. O'BRIEN, G. L. (1980). A limit theorem for sample maxima and heavy branches in Galton-Watson trees. J. Appl. Probab. 17 539-545.