Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Whittle type inequality for demisubmartingales


Author: B. L. S. Prakasa Rao
Journal: Proc. Amer. Math. Soc. 130 (2002), 3719-3724
MSC (2000): Primary 60E15
DOI: https://doi.org/10.1090/S0002-9939-02-06517-6
Published electronically: May 15, 2002
MathSciNet review: 1920053
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A Whittle type inequality for demisubmartingales is derived and a strong law of large numbers for functions of a demisubmartingale is obtained.


References [Enhancements On Off] (What's this?)

  • 1. Christofides, T.C.: Maximal inequalities for demimartingales and a strong law of large numbers, Statist. Probab. Lett., 50 (2000), 357-363. MR 2001m:60032
  • 2. Dufresnoy, J.: Autour de l'inegalite de Kolmogorov, C. R. Acad. Sci. Paris, 264A (1967), 603. MR 37:5909
  • 3. Hajek, J. and Renyi, A.: A generalization of an inequality of Kolomogorov, Acta. Math. Acad. Sci. Hung., 6 (1955), 281-284. MR 17:864a
  • 4. Newman, C.M. and Wright, A.L.: Associated random variables and martingale inequalities, Z. Wahrsch. Verw. Geb., 59 (1982), 361-371. MR 85d:60088
  • 5. Prakasa Rao, B.L.S.: Hajek-Renyi type inequality for associated sequences, Statist. Probab. Lett., 2001 (to appear).
  • 6. Prakasa Rao, B.L.S.: Application of Whittle's inequality for Banach space valued martingales, Statist. Probab. Lett., 2001 (to appear).
  • 7. Prakasa Rao, B.L.S. and Dewan, I.: Associated sequences and related inference problems, In Handbook of Statistics: Stochastic Processes: Theory and Methods, (Edited by D.N. Shanbhag and C.R.Rao), North Holland, Amsterdam, 19 (2001), 693-728. CMP 2002:03
  • 8. Rao, P.: Whittle's inequality in Hilbert space, Theory of Probability and Mathematical Statistics, 16 (1978), 111-116. MR 55:13517
  • 9. Roussas, G.G.: Positive and negative dependence with some statistical applications, In Asymptotics, Nonparametrics and Time Series, (Edited by S.Ghosh), Marcel Dekker, New York, 1999, 757-788. CMP 2000:05
  • 10. Sen, P.K.: A Hajek-Renyi inequality for stochastic vectors with applications to simultaneous confidence regions, Ann. Math. Statist., 42 (1971), 1132-1134.
  • 11. Shixin, Gan.: The Hajek-Renyi inequality for Banach space valued martingales and the $p$ smoothness of Banach spaces, Statist. Probab. Lett., 32 (1997), 245-248. MR 97k:60006
  • 12. Whittle, P.: Refinements of Kolmogorov's inequality, Theory Probab. Appl., 14 (1969), 310-311. MR 39:7657

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60E15

Retrieve articles in all journals with MSC (2000): 60E15


Additional Information

B. L. S. Prakasa Rao
Affiliation: Indian Statistical Institute, 7, SJSS Marg, New Delhi 110 016, India
Email: blsp@isid.ac.in

DOI: https://doi.org/10.1090/S0002-9939-02-06517-6
Keywords: Whittle's inequality, Kolmogorov's inequality, maximal inequality, Hajek-Renyi inequality, Dufresnoy's inequality, demisubmartingale, demimartingale, associated sequences, strong law of large numbers
Received by editor(s): June 15, 2001
Received by editor(s) in revised form: August 3, 2001
Published electronically: May 15, 2002
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society