Some bounds on the rate of convergence in the CLT for martingales. II

Theory of Probability and its Applications

Volumn 44, Issue 3, 1999, Pages 523-536

  Rinott, Y ^a   Rotar, V ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CENTRAL ECONOMICS AND MATHEMATICS INSTITUTE   (Russian Federation)

Author keywords

Central limit theorem; Martingales; Rate of convergence

Indexed keywords

EID: 0033622293     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0040585x97977744     Document Type: Article

References (28)

1. R. N. BHATTACHARYA AND R. RANGA RAO, Normal Approximation and Asymptotic Expansions, Krieger, Melbourne, FL, 1986.
2. E. BOLTHAUSEN, Exact convergence rates in some martingale central limit theorems, Ann. Probab., 10 (1982), pp. 672-688.
3. E. BOLTHAUSEN, The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains, Z. Wahrsch. Verw. Gebiete, 60 (1982), pp. 283-289.
4. R. BRADLEY, Basic properties of strong mixing conditions, in Dependence in Probability and Statistics 11, E. Eberlein and M. Taqqu, eds., Birkhäuser, Basel, 1986, pp. 165-192.
5. A. DVORETZKY, Asymptotic normality for sums of dependent random variables, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, University of California Press, Berkeley, Los Angeles, CA, 1972, pp. 513-535.
6. R. V. ERICKSON, M. P. QUINE, AND N. C. WEBER, Explicit bounds for the departure from normality of sums of dependent random variables, Acta Math. Acad. Sci. Hungar., 34 (1979), pp. 27-32.
7. I. V. EVSTIGNEEV, Regular conditional expectations of random variables depending on parameters, Theory Probab. Appl., 31 (1987), pp. 515-518.
8. I. G. GRAME, Normal approximation for martingales, Soviet Math. Surveys, 42 (1987), pp. 189-190.
9. E. HAEUSLER, On the rate of convergence in the martingale central limit theorem for martingales with discrete and continuous time, Ann. Probab., 16 (1988), pp. 275-299.
10. E. HAEUSLER AND K. Joos, A nonuniform bound on the rate of convergence in the martingale central limit theorem, Ann. Probab., 16 (1988), pp. 1699-1720.
11. P. HALL AND C. C. HEYDE, Martingale Limit Theory and Its Applications, Academic Press, New York, 1980.
12. P. HALL AND C. C. HEYDE, Rates of convergence in the martingale limit theorem, Ann. Probab., 9 (1981), pp. 395-404.
13. C. C. HEYDE AND B. M. BROWN, On the departure from normality of a certain class of martingales, Ann. Math. Statist., 41 (1970), pp. 2161-2165.
14. J. JACOD AND A. N. SHIRYAEV, Limit Theorems for Stochastic Processes, Springer-Verlag, New York, 1987.
15. Y. KATO, Rates of convergence in central limit theorem for martingale differences, Bull. Math. Statist., 18 (1978/79), pp. 1-8.
16. L. V. KIR'YANOVA AND V. I. ROTAR', Estimates for the rate of convergence in the central limit theorem for martingales, Theory Probab. Appl., 36 (1992), pp. 289-302.
17. K. KUBILYUS, On the rate of convergence in the functional limit theorem for semimartingales, Lithuanian Math. J., 25 (1989), pp. 59-69.
18. R. SH. LIPTSER AND A. N. SHIRYAEV, On the rate of convergence in the central limit theorem for semimartingales, Theory Probab. Appl., 27 (1982), pp. 1-13.
19. R. S. LIPTSER AND A. N. SHIRYAEV, Theory of Martingales, Kluwer Academic Publishers, Boston, 1985.
20. T. MORI, On the rate of convergence in the martingale limit theory, Studia Sci. Math. Hungar., 12 (1977), pp. 413-417.
21. S. V. NAGAEV, More exact statements of limit theorems for homogeneous Markov chains, Theory Probab. Appl., 6 (1961), pp. 62-81.
22. M. PELIGRAD, Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (a survey), in Dependence in Probability and Statistics, E. Eberlein and M. Taqqu, eds., Birkhäuser, Basel, 1986, pp. 193-223.
23. Y. RINOTT, On normal approximation rates for certain sums of dependent random variables, J. Comput. Appl. Math., 55 (1994), pp. 135-143.
24. -1/2log n rate, and applications to multivariate graph related statistics, J. Multivariate Anal., 56 (1996), pp. 333-350.
25. V. I. ROTAR, Probability Theory, World Scientific, River Edge, NJ, 1997.
26. V. V. SAZONOV, Normal Approximation - Some Recent Advances, Lecture Notes in Math. 879, Springer-Verlag, Berlin, 1981.
27. C. STEIN, Approximate Computation of Expectations, IMS, Hayward, CA, 1986.
28. A. N. TIKHOMIROV, On the convergence rate in the central limit theorem for weakly dependent random variables, Theory Probab. Appl., 25 (1980), pp. 790-809.