THE UNIFORM CLT FOR MARTINGALE DIFFERENCE OF FUNCTION-INDEXED PROCESS UNDER UNIFORMLY INTEGRABLE ENTROPY

  • Published : 1999.07.01

Abstract

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

Keywords

References

  1. J. Korean Math. Soc. v.32 An Empirical CLT for Stationary Martingale Differences J. Bae
  2. Preprint The Uniform CLT for the Function-Indexed Kaplan-Meier Integral Process
  3. J. Theoret. Probab v.8 Uniform CLT for Markov Chains and Its Invariance Principle: A Martingale Approach J. Bae;S. Levental
  4. Ann. Inst. H. Poincare Probab. Statist v.31 no.5 Invariance principles for absolute regular empirical process P. Doukhan;P. massart;E. Rio
  5. Lecture Notes in Math A Course on Empirical Processes R. M. Dudley
  6. Theory and Examples R. Durrett
  7. Ann. Probab v.3 On Tail Probabilities for Martingales D. Freedman
  8. Aarhus Universitet., Matematisk Institut Stochastic processes on Polish spaces J.Hoffmann-JØrgensen
  9. Sov. Math. Dokl v.19 The Central limit theorem for stationary Markov Processes M. I. Gordin and B. A.;Lifsic, B. A.
  10. J. Amer. Statist. Assoc. v.53 Nonparametric estimation from incomplete observations E. L. Kaplan;P. Meier
  11. J. Theoret. Probab v.2 A Uniform CLT for Uniformly Bounded Families of Martingale Differences S. Levental
  12. Ann. Probab v.15 A Central Limit Theorem under Metric Entropy with L₂ Bracketing M. Ossiander
  13. Springer series in Statistics Convergence of Stochastic Processes D. Pollard
  14. Regional conference series in Probability and Statistics 3, Inst. Math. Statist. Empirical processes: Theory and Applications
  15. Ann. Statist. v.23 The central limit theorem under random censorship W. Stute
  16. Springer series in Statistics Weak Convergence and Empirical Processes with Applications to Statistics A. W. Van der Vaart;J. A. Wellner
  17. J. Multivariate. Anal v.62 Functional Central Limit Theorem for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions K. Ziegler