Selection from a stable box

Bernoulli

Volumn 14, Issue 1, 2008, Pages 125-139

  Aue, Alexander ^a   Berkes, István ^b   Horváth, Lajos ^c  

^a CLEMSON UNIVERSITY   (United States)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^c UNIVERSITY OF UTAH   (United States)

Author keywords

CUSUM; Functional limit theorems; Order statistics; Permutation principle; Stable distributions

Indexed keywords

EID: 41449118528     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ6014     Document Type: Article

References (15)

1. Athreya, K.B. (1987). Bootstrap of the mean in the infinite variance case. Ann. Statist. 15 724-731.
2. Berkes, I. and Philipp, W. (1979). Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7 29-54.
3. Billingsley, P. (1968). Convergence of Probability Measures. New York: Wiley.
4. Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987). Regular Variation. Cambridge Univ. Press.
5. Breiman, L. (1968). Probability. Reading, MA: Addison-Wesley.
6. Csörgo, M., Csörgo, S., Horváth, L. and Mason, D.M. (1986). Normal and stable convergence of integral functions of the empirical distribution function. Ann. Probab. 14 86-118.
7. Feller, W. (1966). An Introduction to Probability Theory and Its Applications. II. New York: Wiley.
8. Hušková, M. (2004). Permutation principle and bootstrap in change point analysis. In Asymptotic Methods in Stochastics (L. Horváth and B. Szyszkowicz, eds.) 273-291. Providence, RI: Amer. Math. Soc.
9. Kasahara, Y. and Watanabe, S. (1986). Limit theorems for point processes and their functionals. J. Math. Soc. Japan 38 543-574.
10. LePage, R., Woodroofe, M. and Zinn, J. (1981). Convergence to a stable distribution via order statistics. Ann. Probab. 9 624-632.
11. Lévy, P. (1931). Sur les séries dont les termes sont des variables éventuelles indépendantes. Studia Mathematica 3 119-155.
12. Petrov, V.V. (1995). Limit Theorems of Probability Theory. Oxford, U.K.: Clarendon.
13. Samorodnitsky, G. and Taqqu, M. (1994). Stable Non-Gaussian Random Processes. New York: Chapman and Hall.
14. Shorack, G. and Wellner, J. (1986). Empirical Processes with Applications to Statistics. New York: Wiley.
15. Zolotarev, V.M. (1986). One-Dimensional Stable Distributions. Providence, RI: Amer. Math. Soc.