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Central Limit Theorem for Self-normalized Weighted Sumsof φ-Mixing Sequences

LIU Ying1, ZHANG Yong2, DONG Zhishan23   

  1. 1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China;3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
  • Received:2007-12-27 Revised:1900-01-01 Online:2008-07-26 Published:2008-07-26
  • Contact: ZHANG Yong

Abstract: Let {Xn, n≥1} be a sequence of strictly stationary φ-mixing random variables with EX=0, V2n be an array of real numbers with under general conditions, we obtained the central limit theorem for selfnormalized weighted sum of {Sn/Vn, n≥1}. The results about this scope are improved and extended.

Key words: φ-mixing sequence, selfnormalized, weighted sums, central limit theorem

CLC Number: 

  • O211.4