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Tightness bounds for strongly mixing random sequences
Author(s):
Richard
C.
Bradley
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1481-1486.
MSC (2000):
Primary 60G10;
Secondary 60G07
Posted:
October 5, 1999
MathSciNet review:
1676307
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Abstract:
For a given strictly stationary, strongly mixing random sequence for which the distributions of the partial sums are tight, certain ``tightness bounds" exist which depend only on the marginal distribution and the mixing rate.
References:
- [1]
- R.C. Bradley, On the dissipation of partial sums from a stationary strongly mixing sequence, Stochastic Process. Appl. 54 (1994), 281-290. MR 95j:60054
- [2]
- R.C. Bradley, On a theorem of K. Schmidt, Statist. Probab. Letters 24 (1995), 9-12. MR 96g:60048
- [3]
- R.C. Bradley, On quantiles and the central limit question for strongly mixing sequences, J. Theor. Probab. 10 (1997), 507-555. MR 98h:60024
- [4]
- H. Dehling, M. Denker, and W. Philipp, Central limit theorems for mixing sequences of random variables under minimal conditions, Ann. Probab. 14 (1986), 1359-1370. MR 88d:60065
- [5]
- M. Denker, Uniform integrability and the central limit theorem for strongly mixing processes, Dependence in Probability and Statistics (E. Eberlein, M.S. Taqqu, eds.), pp.269-274, Birkhäuser, Boston, 1986. MR 88h:60044
- [6]
- N. Herrndorf, Stationary strongly mixing sequences not satisfying the central limit theorem, Ann. Probab. 11 (1983), 809-813. MR 84m:60030
- [7]
- T. Mori and K. Yoshihara, A note on the central limit theorem for stationary strong-mixing sequences, Yokohama Math J. 34 (1986), 143-146. MR 88g:60068
- [8]
- M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Natl. Acad. Sci. U.S.A. 42 (1956), 43-47. MR 17:635b
- [9]
- K. Schmidt, Cocyles on Ergodic Transformation Groups, Macmillan, Delhi, 1977. MR 58:28262
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Additional Information:
Richard
C.
Bradley
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405-5701
Email:
bradleyr@indiana.edu
DOI:
10.1090/S0002-9939-99-05404-0
PII:
S 0002-9939(99)05404-0
Keywords:
Strictly stationary,
strong mixing,
tightness
Received by editor(s):
June 25, 1998
Posted:
October 5, 1999
Additional Notes:
This work was partially supported by NSF grant DMS 9703712.
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
2000,
American Mathematical Society
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