Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (2): 267-275.

• Articles • Previous Articles     Next Articles

A Note on Strong Approximation for Trimmed Sums

 FU Ke-Aong   

  1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
  • Received:2011-01-07 Revised:2012-11-06 Online:2013-04-25 Published:2013-04-25
  • Supported by:

    国家自然科学基金(11126316, 11101364, 11201422, 10901138)和浙江省自然科学基金(LQ12A01018, Q12A010066,  Y6110110)资助

Abstract:

Let {X, Xn; n≥1} be a sequence of independent and identically distributed random variables, and let Xn(r)}=Xm if |Xm| is the r-th maximum of {|Xk|; kn} . Define Sn==∑k=1nXk and (r)Sn=Sn-(Xn(1)+…+Xn(r)). This paper aims to establish a general strong approximation for the trimmed sums (r)Sn without variance, and as applications, general functional laws of the iterated logarithm for trimmed sums and products of trimmed sums are derived.

Key words: Strong Approximation, Trimmed sums, Product, Functional law of the iterated , logarithm

CLC Number: 

  • 60F15
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