Author: Ke-Ang Fu 1
View More View Less
  • 1 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
Restricted access

Abstract

Let {X,X n; n≧1} be a sequence of B-valued i.i.d. random variables. Denote if ∥X m∥ is the r-th maximum of {∥X k∥; kn}, and let be the trimmed sums, where . Given a sequence of positive constants {h(n), n≧1}, which is monotonically approaching infinity and not asymptotically equivalent to loglogn, a limit result for is derived.

  • [1] Zhang, L. X. 2002 Strong approximation theorems for sums of random variables when extreme terms are excluded Acta Math. Sinica, English Series 18 311326 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2] Zhang, L. X. 2002 LIL and the approximation of rectangular sums of B-valued random variables when extreme terms are excluded Acta Math. Sinica, English Series 18 605614 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [3] Fu, K. A. Zhang, L. X. 2009 A general LIL for trimmed sums of random fields in Banach spaces Acta Math. Hungar. 122 91103 .

  • [4] Klesov, O. Rosalsky, A. 2001 A nonclassical law of the iterated logarithm for i.i.d. square integrable random variables Stochastic Anal. Appl. 19 627641 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [5] Klesov, O. Rosalsky, A. 2002 A nonclassical law of the iterated logarithm for i.i.d. square integrable random variables. II Stochastic Anal. Appl. 20 839846 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [6] Huang, W. 2004 A nonclassical law of the iterated logarithm for functions of negatively associated random variables Stochastic Anal. Appl. 22 657678 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [7] Wang, J. F. Zhang, L. X. 2006 A nonclassical law of the iterated logarithm for functions of positively associated random variables Metrika 64 361378 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [8] Einmahl, U. Mason, D. M. 1997 Gaussian approximation of local empirical processes indexed by functions Probab. Theory Relat. Fields 107 283311 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [9] Bingham, N. H. Goldie, C. M. Teugels, J. L. 1987 Regular Variation Cambridge University Press Cambridge.

  • [10] Ledoux, M. Talagrand, M. 1991 Probability in Banach Spaces Springer New York.

  • [11] Feller, W. 1968 An Introduction to Probability Theory and Its Applications 3 1 Wiley New York.